Thinking Mathematically Logic 3.4 Truth Tables for the Conditional and Biconditional.

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Thinking Mathematically Logic 3.4 Truth Tables for the Conditional and Biconditional

The Definition of the Conditional A conditional statement is false only when the antecedent (the “if” part) is true and the consequent (the “then” part) is false.

Example: The Conditional Exercise Set 3.4 #3 Construct a truth table for the statement ~(q  p)

The Definition of the Biconditional A biconditional statement is true only when the component statements have the same truth value. p  q is equivalent to (p  q) ^ (q  p)

Example: Biconditional Exercise Set 3.4 #21 Construct a truth table for (p  q)  p

A tautology is a statement that is always true. All entries in the final column of the truth table are T A self-contradiction is a compound statement that is false in all possible cases. All entries in the final column of the truth table are F Definition Tautology / Self Contradiction

Example: Tautology/Self- Contradiction Exercise Set 3.4 #35, 41 Construct a truth table to determine if the following statement is a tautology or self- contradiction. [(p  q) ^ ~q]  ~p (p ^ q) ^ (~p V ~q)

Thinking Mathematically Logic 3.4 Truth Tables for the Conditional and Biconditional