Truth Table Practice — In which row will the p → q operation be false?

The implication (p → q) is false only if p is true (1) but q is false (0).

Truth Tables

Logical Operators Tautology and Contradiction

A truth table shows what result a logical operation gives in every possible case. The rows of the table contain all combinations of true-false for the statements.

Negation (¬)

If p is true (1), then ¬p is false (0). If p is false (0), then ¬p is true (1).

Conjunction (∧)

The "AND" operation is true only if both are true.

Disjunction (∨)

The "OR" operation is false only if both are false. It is true in all other cases.

Implication (→)

The "if p, then q" is false only if p is true but q is false.

Equivalence (↔)

The "if and only if" operation is true if p and q take the same truth value.

Summary

Truth tables provide a simple way to see when a complex statement is true or false. With their help, the operation of any logical operation is completely transparent.

Practice Exercise

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