Contrapositive Statement
If not q, then not p
A contrapositive statement is a proposition that has the same meaning as a conditional statement, but with the if and then clauses switched and negated. For example, the contrapositive statement of If it is raining, then the ground is wet is If the ground is not wet, then it is not raining.
The contrapositive statement preserves the logical equivalence of the original statement, meaning that if the original statement is true, then its contrapositive statement is also true. In fact, one way to prove the validity of a conditional statement is to show that its contrapositive statement is also true.
The contrapositive statement is important because it allows one to reason about a statement in a different way and potentially arrive at a different understanding than the original statement. It also helps to recognize the symmetry between the if and then clauses in a conditional statement.
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