Use a truth table to determine whether the following statement is a contradiction, a tautology or neither. if it is a contradiction or a tautology, verify your answer using logical equivalences. ((p ∨ q) ∧ (p → r) ∧ (∼ r)) → q

The statement is a tautology.

Step-by-step explanation:

A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.

We can see from the truth table that the last column contains only true values. Therefore, the statement is a tautology.

Logical equivalences are a type of relationship between two statements or sentences in propositional logic. To simplify an equivalency, start with one side of the equation and attempt to replace sections of it with equivalent expressions. Continue doing this until you have achieved the desired statement form.

by implication law

by implication law

by de Morgan’s law

by Double Negative

by de Morgan’s law

by commutative and associative laws

by distributive laws

by negation and identity laws

by communicative and associative laws

by negation and domination laws

Therefore, the statement is a tautology.

answer:

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step-by-step explanation:

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