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# 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_)