Thinking Mathematically

1
Thinking Mathematically

• Truth Tables for the Conditional and Biconditional

2
When is a conditional Statement true?

• We have discussed the idea of implication.
• If p then q. For example
• If it rains then driveway gets wet.
• What should the truth table for implication be?

3
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.
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A Statement That Is Equivalent to the Conditional

• The truth value of a conditional statement does
  not change if the antecedent and consequent are
  reversed and both are negated.
• Examples
• Do a truth table to verify this.

5
The Definition of the Biconditional
A biconditional statement is true only when the
antecedent (the if part) and the consequent
(the then part) have the same truth value.
6
Definition of a Tautology
A tautology is a statement that is always true.