What Contrapositive is
Contrapositive is a method of proof used in mathematics, which involves taking the inverse of a statement and then inverting the terms. It is used to prove that a statement is true by proving the contrapositive of the statement.
The steps for proving the contrapositive of a statement are as follows:
- Start by writing the statement in its original form.
- Take the inverse of the statement by switching the terms from positive to negative and vice versa.
- Prove the inverse of the statement by using logical reasoning and appropriate evidence.
- Once the inverse of the statement is proven, the original statement is automatically true.
Examples
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If a sample has a mean of 10, then it cannot have a mean greater than 12. (Contrapositive: If a sample has a mean greater than 12, then it cannot have a mean of 10.)
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If a sample has a variance of 25, then it cannot have a variance less than 15. (Contrapositive: If a sample has a variance of less than 15, then it cannot have a variance of 25.)