Truth Tables
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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