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Converse, Inverse, Contrapositive

Given a conditional statement "if p, then q" 

If it rains, then they cancel school.

To form the converse of the conditional statement, switch the hypothesis and the conclusion: "if q, then p"

If they cancel school, then it rains.

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion: if not q, then not p"

If it does not rain, then they do not cancel school.

To form the contrapositive of the conditional statement, switch the hypothesis and the conclusion of the inverse statement: "if not p, then not q."            

If they do not cancel school, then it does not rain.

Statement If p, then q.
Converse If q, then p.
Inverse If not p, then not q.
Contrapositive If not q, then not p.

One important rule of logic to remember: 

If the statement is true, then the contrapositive is also logically true.

And by this rule, we can also have: if the converse is true, then the inverse is also logically true.


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