What isn't the inverse of this statement(?)
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It is what you get in an inference, after negating both sides. That is, if you have a statement such as: if a then b the inverse of this statement is: if not a then not b Note that the inverse is NOT equivalent to the original statement.
Inverse
An Inverse statement is one that negates the hypothesis by nature. This will result into negation of the conclusion of the original statement.
x=y is the identity. It is its own inverse. So the inverse is y=x.
The statement formed when you negate the hypothesis and conclusion of a conditional statement. For Example: If you had enough sleep, then you did well on the test. The inverse will be: If you didn't have enough sleep, then you didn't do well on the test.