- Which of the following sentences are propositions? What are the truth values of those that are propositions?
- Richmond is the capital of Virginia.
- 2 + 3 = 7.
- Open the door.
- 5 + 7 < 10.
- The moon is a sattelite of the earth.
*x*+ 5 = 7.*x*+ 5 > 9 for every real number*x*.

- What is the negation of each of the following propositions?
- Norfolk is the capital of Virginia.
- Food is not expensive in the United States.
- 3 + 5 = 7.
- The summer in Illinois is hot and sunny.

- Let
*p*and*q*be the propositions:*p*: Your car is out of gas.*q*: You can't drive your car. Write the following propositions using*p*and*q*and logical connectives.- Your car is not out of gas.
- You can't drive your car if it is out of gas.
- Your car is not out of gas if you can drive it.
- If you can't drive your car then it is out of gas.

- Determine whether each of the following implications is true or false.
- If 0.5 is an integer, then 1 + 0.5 = 3.
- If cars can fly, then 1 + 1 = 3.
- If 5 > 2 then pigs can fly.
- If 3*5 = 15 then 1 + 2 = 3.

- State the converse and contrapositive of each of the following implications.
- If it snows today, I will stay home.
- We play the game if it is sunny.
- If a positive integer is a prime then it has no divisors other than 1 and itself.

- Construct a truth table for each of the following compound propositions.
*p**p*- (
*p**q*)*q* - (
*p**q*) (*q**p*)

# Homework Assignment 2

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