# 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_ !and.gif! !not.gif! _p_

## (_p_ !or.gif! !not.gif! _q_) !imp.gif! _q_

## (_p_ !imp.gif! _q_) !eqv.gif! ( !not.gif! _q_ !not.gif! _p_)

## 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_ !and.gif! !not.gif! _p_

## (_p_ !or.gif! !not.gif! _q_) !imp.gif! _q_

## (_p_ !imp.gif! _q_) !eqv.gif! ( !not.gif! _q_ !not.gif! _p_)