# Why is a conditional true when the antecedent is false?

## Why is a conditional true when the antecedent is false?

When the antecedent is false, the truth value of the consequent does not matter; the conditional will always be true. A conditional is considered false when the antecedent is true and the consequent is false….Conditional.

P Q P ⇒ Q
F F T

### Why is implication true when p is false?

An implication is the compound statement of the form “if p, then q.” It is denoted p⇒q, which is read as “p implies q.” It is false only when p is true and q is false, and is true in all other situations.

#### Is it possible to have a series of true conditional statements that lead to a false conclusion?

The logical connector in a conditional statement is denoted by the symbol . The conditional is defined to be true unless a true hypothesis leads to a false conclusion….

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Given: p: 72 = 49. true
s: A square is not a quadrilateral. false
Problem: Write each conditional below as a sentence. Then indicate its truth value.

When the antecedent condition is false the consequent must also be false?

A conditional asserts that if its antecedent is true, its consequent is also true; any conditional with a true antecedent and a false consequent must be false. For any other combination of true and false antecedents and consequents, the conditional statement is true.

What makes a conditional false is a false antecedent and a false consequent?

Conditional statement: an “if p, then q” compound statement (ex. A conditional asserts that if its antecedent is true, its consequent is also true; any conditional with a true antecedent and a false consequent must be false.

## What is the truth value of the conditional statement when the hypothesis is true and the conclusion is false?

The conditional statement P→Q means that Q is true whenever P is true. It says nothing about the truth value of Q when P is false. Using this as a guide, we define the conditional statement P→Q to be false only when P is true and Q is false, that is, only when the hypothesis is true and the conclusion is false.