# Logic Problems

1. Determine whether ~ [~ (p V ~q) <=> p V ~q. Explain the method(s) you used to determine your answer.

2. Translate the following argument into symbolic form. Determine whether the argument is valid or invalid. You may compare the form of the argument to one of the standard forms or use a truth table.

If Spielberg is the director, then the movie should be good.

Spielberg didn’t direct the movie, so it probably isn’t good.

4. Construct one truth table that contains truth values for all of the given statements and determine which of the statements, if any, are logically equivalent.

(a) (~p) V (~q) (b) (~p) ^ (~q) (c) ~(p V q)

5. Use the following statements for p and q to illustrate De Morgan’s laws.

p: The moon is round

q: The night is dark.

6) Use Euler diagrams to determine the validity of the arguments

All squares are rectangles

All rectangles are quadrilaterals

Some quadrilaterals are equilateral

Therefore, all squares are equilateral.