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3.3 – The Conditional

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 .”.

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3.3 – The Conditional

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

  3. 3.3 – The Conditional Special Characteristics of Conditional Statementsfor a Truth Table “If you participate in class, then you will get extra points."  If the antecedent is false, then p → qis automatically true. If you do not participate in class (false), the truthof 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. If you do not participate in class (false), then you do not get extra points. The teacher's statement is true in both cases.

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

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

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