Converse
The converse of a conditional statement is formed by interchanging the hypothesis and conclusion of the original statement.
In other words, the parts of the sentence change places.
The words “if” and “then” do not move.
Example:
- Conditional: “If the space shuttle was launched, then a cloud of smoke was seen.”
- Converse: “If a cloud of smoke was seen, then the space shuttle was launched.”
HINT: Try to associate the logical CONVERSE with Converse™ sneakers — think of the two parts of the sentence “putting on their sneakers” and “running” to their new positions.
It is important to remember that the converse does NOT necessarily have the same truth value as the original conditional statement.
Consider:
- Conditional: “If the space shuttle was launched, then a cloud of smoke was seen.” This statement is true since the exhaust from the shuttle creates a cloud of smoke.
- Converse: “If a cloud of smoke was seen, then the space shuttle was launched.” This statement is not always true since many other events (a fire, a running herd of buffalo, car exhaust, etc.) could have caused a cloud of smoke.
An interesting fact: The converse has the same truth value as the inverse of the original statement. The CONVERSE and the INVERSE 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 |