Math

Math 1501 Homework#1 There is not enough room to complete the assignment on this page. You must complete the homework on a separate sheet(s) of paper. To get full credit for this assignment you must show all the work and your work must be neat and easy to follow.

3.1 1. Write the negation of the following statement:

All pigs fly.

2. Let p and q represent the following simple statements. p: The play is boring. q: The chair is broken. Write the following statement in its symbolic form. The play is boring and the chair is not broken.

3. Let p and q represent the following simple statements. p: The stove is hot. q: I work hard. Write the following statement in its symbolic form. If the stove is not hot, then I do not work hard.

4. Let p and q represent the following simple statements. p: The fish is slimy. q: The boat is big. Write the following statement in its symbolic form. It is false that the fish is slimy or the boat is big.

3.2 5. Construct a truth table for ~ p∧q

6. Construct a truth table for ~ p ∨~ q 7. Construct a truth table for ~ (~ p ∨q) 8. Construct a truth table for q ∨(~ p ∧r) 9. Write the following compound statement in symbolic form and construct a truth able.

p: The rice has been cooked. q: The lemonade is cold. “The rice has been cooked and the lemonade is cold.”

3.3

Construct a truth table for the following. 10. ~ p ⇔q

11. ~ p→ q 12. (p →q)⇔ p 13. q →( p→ ~q) 14. 14.(p ∨q)⇔( p∧q)

Determine whether the statement is a tautology, self-contradiction, or neither. 15. ( ~ p →q)∨~q 16. (p ∨q)∧(~ p ∧~ q)