Inverse
The inverse of a conditional statement is formed by negating the hypothesis and negating the conclusion of the original statement.
In other words, the word “not” is added to both parts of the sentence.
Example:
- Conditional: “If you grew up in Alaska, then you have seen snow.”
- Inverse: “If you did not grow up in Alaska, then you have not seen snow.”
HINT: Remember that to create an Inverse, you will need to Insert the word NOT into both portions of the sentence. Since you are actually negating each part of the sentence, you may also use other words (in addition to NOT) to create the negation.
It is important to remember that the inverse does NOT necessarily have the same truth value as the original conditional statement.
Consider:
- Conditional: “If you grew up in Alaska, then you have seen snow.”
Considering the climatic conditions in Alaska, this statement is true. - Inverse: “If you did not grow up in Alaska, then you have not seen snow.” Considering that there are other areas in the world that have snow (such as New York state), this statement is false.
An interesting fact: The inverse has the same truth value as the converse of the original statement. The INVERSE and the CONVERSE of the original statement are logically equivalent.
(“equivalent” means “the same”)
A truth table clearly shows the relationship between the conditional, the converse, and the inverse:
| Conditional | Converse | Inverse | ||||
| p | q | ∼p | ∼q | p → q | q → p | ∼p → ∼q |
| T | T | F | F | T | T | T |
| T | F | F | T | F | T | T |
| F | T | T | F | T | F | F |
| F | F | T | T | T | T | T |