DISCRETE STRUCTURES
Ch-4 Homework
Directions: Answer all questions and double check your answers. After you feel comfortable with your answers, go to the content folder and click on HW-4_Logic to post your answers on blackboard. Make sure to submit your answers before the due date, you also need to allow yourself enough time (60 to 90 minutes) to submit your answers. When you start you must complete answering all questions. Questions and answers will be in the forms of True/False, Multiple Choice, and multiple answers. This will allow you to compare the answers you have with the different options on blackboard. Notice questions on blackboard may not have matching numbers with the following questions. Some of the following questions could be broken into multiple questions.
For problems (1-5):
Let proposition p be false, proposition q be true, proposition r be false, and proposition s be true. Determine whether each of these propositions is true or false, show your work:
1.
2.
3.
4.
5.
Write a truth table for each proposition in problems 6-10, then compare to possible solution, the possible solution could be correct or it could be wrong. If wrong you need to identify errors:
6.
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p
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q
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q
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p
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T
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T
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F
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F
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T
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F
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T
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T
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F
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T
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F
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F
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F
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F
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T
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F
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Possible Solution?
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7.
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p
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q
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p
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p˄q
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¬p˅q
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(p˄q)˅(¬p˅q)
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T
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T
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T
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F
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F
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T
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F
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F
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p
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q
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p
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p˄q
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¬p˅q
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(p˄q)˅(¬p˅q)
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T
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T
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F
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T
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T
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F
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T
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F
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F
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F
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F
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T
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F
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T
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T
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F
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T
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F
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F
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F
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T
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F
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T
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F
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Possible Solution?
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8.
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p
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q
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r
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q
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p˄q
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¬(p˄q)
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(¬q˅r)
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¬ (p˄q)˅(¬q˅r)
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T
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T
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T
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T
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T
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F
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T
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F
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T
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T
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F
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F
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F
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T
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T
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F
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T
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F
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F
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F
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T
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F
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F
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F
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p
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q
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r
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q
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p˄q
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¬(p˄q)
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(¬q˅r)
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¬ (p˄q)˅(¬q˅r)
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T
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T
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T
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F
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T
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F
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F
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F
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T
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T
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F
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F
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T
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F
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T
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T
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T
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F
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T
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T
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F
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T
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F
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F
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T
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F
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F
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T
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F
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T
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F
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F
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F
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T
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T
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F
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F
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T
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F
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F
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F
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T
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F
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F
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F
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T
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T
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F
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F
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F
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T
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T
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F
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T
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F
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F
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F
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F
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F
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T
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F
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T
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F
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F
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Possible Solution?
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9.
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p
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q
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r
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p˄r
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(p˄r)⟶q
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T
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T
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T
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T
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T
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F
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T
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F
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T
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T
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F
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F
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F
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T
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T
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F
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T
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F
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F
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T
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F
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F
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F
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q
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r
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p˄r
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(p˄r)⟶q
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T
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T
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T
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T
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T
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T
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T
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F
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F
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T
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T
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F
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T
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T
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F
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T
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F
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F
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F
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T
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F
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T
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T
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F
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T
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F
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T
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F
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F
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T
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F
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F
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T
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F
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T
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F
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F
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F
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F
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T
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Possible Solution?
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10.
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p
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q
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r
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p˄q
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(p˄q)⟷ r
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T
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T
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T
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T
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T
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F
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T
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F
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T
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T
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F
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F
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F
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T
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T
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F
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T
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F
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F
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T
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F
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F
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F
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p
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q
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r
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p˄q
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(p˄q)⟷ r
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T
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T
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T
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T
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T
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T
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T
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F
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T
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F
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T
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F
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T
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F
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F
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T
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F
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F
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F
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F
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F
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T
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T
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F
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F
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F
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T
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F
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F
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F
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F
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F
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T
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F
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F
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F
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F
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F
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F
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F
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Possible Solution?
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For problems 11-16, refer to the propositions p, q, and r; where p is true, q is false, and r’s status is unknown at the time. Tell whether each proposition is true, is false, or has an unknown status at the time:
11.
12.
13.
14.
15.
16.
For problems 17-20,
consider propositions P and Q, and state whether . You could use the truth table method shown in class.
17. ,
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P= p
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q
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Q=p˅q
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T
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T
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T
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F
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F
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T
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F
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F
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18. ,
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p
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q
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p
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P = p⟶q
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Q = ¬p˅q
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T
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T
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F
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T
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F
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F
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F
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T
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T
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F
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F
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T
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19. ,
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p
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q
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r
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p⟶q
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q⟶r
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P= (p⟶q) ˄ ( q⟶r)
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Q = p⟶r
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T
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T
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T
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T
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T
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T
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T
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F
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T
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F
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T
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F
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T
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F
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T
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T
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F
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F
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F
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T
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F
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T
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T
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T
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T
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F
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T
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F
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T
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F
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F
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F
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T
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T
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T
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F
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F
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F
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T
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T
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20. ,
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p
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q
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r
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p⟶q
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P= (p⟶q)⟶r
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( q⟶r)
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Q=p⟶( q⟶r)
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T
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T
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T
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T
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T
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T
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F
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T
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T
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F
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T
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F
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T
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F
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F
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F
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F
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T
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T
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T
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F
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T
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F
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T
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F
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F
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T
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T
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F
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F
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F
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T
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Page | 6
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