1. 3.3 – The Conditional A conditional statement is a compound statement that uses the connective if…then. The conditional is written with an arrow, so “if p then q” is symbolized The conditional is read as “p implies q” or “if p then q.” The statement p is the antecedent, while q is the consequent.

2. Special Characteristics of Conditional Statements for a Truth Table 3.3 – The Conditional When the antecedent is true and the consequent is true, p → q is true. Teacher: “If you participate in class, then you will get extra points." If you participate in class (true) and you get extra points (true) then, The teacher's statement is true. If you participate in class (true) and you do not get extra points (false), then, The teacher’s statement is false. When the antecedent is true and the consequent is false, p → q is false.

3. Special Characteristics of Conditional Statements for a Truth Table 3.3 – The Conditional If the antecedent is false, then p → q is automatically true. “If you participate in class, then you will get extra points." If you do not participate in class (false), the truth of the teacher's statement cannot be judged. The teacher did not state what would happen if you did NOT participate in class. Therefore, the statement has to be “true”. If you do not participate in class (false), then you get extra points. The teacher's statement is true in both cases. If you do not participate in class (false), then you do not get extra points.

4. Truth Table for The Conditional p qp → q T TT T FF F TT F FT If p, then q 3.3 – The Conditional A tautology is a statement that is always true, no matter what the truth values of the components are.

5. Examples: Decide whether each statement is True or False T → (4 < 2) 3.3 – The Conditional (T represents a true statement, F a false statement). T → F F (8 = 1) → F F → F T F → (3 ≠ 9) F → T T