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Truth Tables and Translation in Symbolic Form

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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.

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The solution contains the answers to various questions in mathematical logic concerning De Morgan's Laws, validity of arguments, symbolic forms etc.

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Translate the argument into symbolic form and (b) determine if the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.
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