Understanding the Implication Operator → in Logic | Definition, Truth Table, and Examples

p → q

In logic, the symbol “→” represents an implication or conditional statement

In logic, the symbol “→” represents an implication or conditional statement. It is read as “if p, then q” or “p implies q”. Here, “p” and “q” represent two logical statements.

In an implication, the statement “p” is called the antecedent or premise, while the statement “q” is called the consequent or conclusion. The implication “p → q” asserts that whenever the antecedent “p” is true, the consequent “q” must also be true.

The truth value of an implication depends on the truth values of its antecedent and consequent. An implication “p → q” is considered true if the antecedent “p” is false or if both “p” and “q” are true. It is only false when the antecedent “p” is true and the consequent “q” is false.

Therefore, the implication “p → q” can be summarized using a truth table as follows:

| p | q | p → q |
|—|—|——-|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |

In the truth table, “T” represents true, and “F” represents false.

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