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Question
Write the converse, inverse and contrapositive of the following statement.
“If it rains then the match will be cancelled.”
Solution
Let
p : It rains,
q : the match will be cancelled.
The symbolic form of the given statement is p → q.
Converse: q → p
i.e., If the match is cancelled then it rains.
Inverse: ~p → ~q
i.e., If it does not rain then the match will not be cancelled.
Contrapositive: ~q → ~p
i.e. If the match is not cancelled then it does not rain.
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