Recognizing Equivalence — Which expression is equivalent to p → q?

The statement p → q always has the same truth value as ¬p ∨ q, so they are equivalent.

Logical Equivalence

Tautology and Contradiction Normal Forms

Two logical expressions are called equivalent if they have the same truth value in every possible case. In this case, the two statements can be interchanged.

Notation

p ≡ q means that p and q have the same truth value in every case.

Example of Equivalent Statements

"If p, then q" is equivalent to "not p or q". For any p and q, they have the same truth value.

Truth Table Example

It is visible that the two expressions give the same value in every row → therefore they are equivalent.

Why is it Important?

Equivalence helps simplify logical expressions. If two statements are equivalent, we can use either one instead of the other, and the result will be the same.

Summary

Two expressions are equivalent if they give the same truth value in every case. This is denoted by ≡. For example: p → q ≡ ¬p ∨ q.

Practice Exercise

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