Math

CSC175 Practice Assignment 3 Type Name:

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1) Given the following propositions, write out the English sentences for the given the symbolic forms. = Jim likes mathematics = Jim likes computer science = Jim likes Sudoku puzzles

a) b) c)

2) Given the following English sentences which are compound propositions, label each simple proposition with a variable and then give the symbolic form. Each simple proposition should NOT include the word “not” in it.

a) 209 is not a prime number and 347 is a prime number. b) If 101 is a prime number, then 347 is a prime number or 209 is a not prime number. c) 347 is a prime number and 101 is not a prime number if and only if 209 is a prime number or 347 is not a prime number. d) 347 is a prime number if 101 is not a prime number.

3) Write the negation of each compound proposition as an English sentence.

a) If mom wants to go to Disneyland then dad will pay for it. b) The kids want to go to Disneyland and dad does not want to pay for it. c) If dad wants to go to the Super Bowl, then the kids can’t go to Disneyland or mom needs a second job.

4) Find the complete truth table for each compound sentence. Be such to order the columns as shown in discussion and in the videos. Use the table builder in the INSERT tab.

a) b) c) d)

5) Use a truth table to determine if is a tautology, contradiction, or neither. Show the complete truth table and explain why you believe your answer is correct.

6) Use a truth table to determine if is equivalent to . Show the complete truth table and explain why you believe your answer is correct.

7) Name the law (or laws if two are used) from pages 58-59 that is used in each equivalence. (DO NOT CREATE A TRUTH TABLE.)

a) b) c) d) e)