Inverse

Definition

The inverse of a statement is formed by negating both the hypothesis and the conclusion. If the original statement is 'If P, then Q,' its inverse is 'If not P, then not Q.'

5 Must Know Facts For Your Next Test

1. The inverse of a conditional statement does not necessarily have the same truth value as the original statement.
2. Both the inverse and converse of a statement are logically equivalent to each other.
3. To form the inverse, both parts of the original conditional (the hypothesis and conclusion) must be negated.
4. An inverse can help in understanding logical equivalence when paired with contrapositive and converse statements.
5. In symbolic logic, if the original statement is represented as P → Q, its inverse is ¬P → ¬Q.

Review Questions

• How do you form the inverse of a conditional statement?
• Is the inverse of a statement always true if the original statement is true?
• What relationship exists between an inverse and a converse?

Related terms

Conditional Statement: A logical statement that has two parts, a hypothesis and a conclusion.

Contrapositive:

Formed by negating both the hypothesis and conclusion of the converse; it always has the same truth value as the original conditional.

Converse:

Formed by swapping the hypothesis and conclusion of an original conditional statement.