Use truth tables to show that the following pairs of expressions are logically equivalent.

(a) p ↔ q and (p → q) ∧ (q → p)

(b) ¬(p ↔ q) and ¬p ↔ q

(c) ¬p → q and p ∨ q

A truth table is a tabular representation of all the combinations of values for inputs and their corresponding outputs. It is a mathematical table that shows all possible outcomes that would occur from all possible scenarios that are considered factual, hence the name. Truth tables are usually used for logic problems as in Boolean algebra and electronic circuits.

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Use truth tables to show that the following pairs of expressions are logically equivalent. (a) p ↔ q and (p → q) ∧ (q → p) (b) ¬(p ↔ q) and ¬p ↔ q (c) ¬p → q and p ∨ q

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Use truth tables to show that the following pairs of expressions are logically equivalent.

(a) p ↔ q and (p → q) ∧ (q → p)

(b) ¬(p ↔ q) and ¬p ↔ q

(c) ¬p → q and p ∨ q