The negation of a statement p is the opposite of the statement. The symbol is
Statement | How to Write It | Example | Symbols | How to Read it |
---|---|---|---|---|
Conditional | Use the given hypothesis and conclusion. | If
|
|
If p, then q. |
Converse | Exchange the hypothesis and the conclusion. | If
|
|
If q, then p. |
Inverse | Negate both the hypothesis and the conclusion of the conditional. | If
|
|
If not p, then not q. |
Contrapositive | Negate both the hypothesis and the conclusion of the converse. | If
|
|
If not q, then not p. |
Below are the truth values of the related statements above. Equivalent statements have the same truth value.
Statement | Example | Truth Value |
---|---|---|
Conditional | If
|
True |
Converse | If
|
False |
Inverse | If
|
False |
Contrapositive | If
|
True |
A conditional and its contrapositive are equivalent statements. They are either both true or both false. The converse and inverse of a statement are also equivalent statements.