Why is a conditional true when the antecedent is false?
Table of Contents
- 1 Why is a conditional true when the antecedent is false?
- 2 Why is implication true when p is false?
- 3 Is it possible to have a series of true conditional statements that lead to a false conclusion?
- 4 What is the truth value of the conditional statement when the hypothesis is true and the conclusion 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….
| 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.