math homework

MAT-130 Homework 3 Name:_________________________________ Due Friday, April 2, 2021, no later than 4:45 P.M. Decide whether each statement is true or false. (1 point each)

1. If ¬(𝑝 ∧ 𝑞) is true, then the truth values of p and q must be both true.

2. p → q is equivalent to ¬ 𝑝 ∨ 𝑞 . Decide whether each is a statement or is not a statement. Note: a compound statement is still a statement. (1 point each) 3. 12 − 24 ≤ 12

4. I command you to drive to Houston, Texas.

Write a negation of the following without using a slash symbol. (1 point each)

5. z > −28

6. 𝑧 − 2 ≤ −37

Construct a truth table for the following compound statement. (4 points) Please show all columns, just as in the class notes. 7. 𝑞 → ¬𝑝 → 𝑞