1. Indicate clearly which of the following are propositions

a. Miss Piggy for President!

b. If x is an odd integer, then for some integer k, x = 2k.

c. The first human to set foot on the moon was Neil Armstrong.

d. 4 x -7 = 10.

e. If a function f from the real numbers to the real numbers is continuous, then f is differentiable.

2. Define the following propositions:

p : My flight is delayed.

q : There are thunderstorms at the airport.

r : The airport has WiFi.

Translate the following English sentences into logical expressions using the definitions above.

a. My flight is not delayed, but the airport doesn't have Wi-Fi, and there are thunderstorms at the airport.

b. My flight is delayed only if there are thunderstorms at the airport.

c. The airport doesn't have Wi-Fi and there are thunderstorms at the airport, but my flight is not delayed.

d. If there are no thunderstorms at the airport, then my flight is not delayed.

e. My flight is not delayed only if there are no thunderstorms at the airport.

3. Let the domain for the variables x and y be all people in our IST 230 class. Define the predicate K(x,y) to mean "x knows y." Express the following sentences with quantified logical expressions.

a. There is someone in our IST 230 class who knows everybody in our IST 230 class.

b. Nobody in our IST 230 class knows anyone in our IST 230 class.

c. Nobody in our IST 230 class knows everyone in our IST 230 class.

d. There is someone in our IST 230 class whom everyone in our IST 230 class knows.

e. Someone in our IST 230 class knows someone in our IST 230 class.

4. Let cbe a proposition that is always false, and let pbe any proposition. Complete the truth table below for

c --> p.

c	p	c --> p

Explain in words what the (correctly completed) truth table for c -->p shows.

5. Prove or Disprove (making sure your proof consists of complete sentences that justify any steps and claims that are not obvious): If x and y are even integers, then x+y is an even integer.