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Question
Write the converse, inverse, contrapositive of the following statement.
If I do not work hard, then I do not prosper.
Solution
Let p : I do not work hard.
q : I do not prosper.
∴ The given statement is p → q.
Its converse is q → p.
If I do not prosper then I do not work hard.
Its inverse is ~p → ~q.
If I work hard then I prosper.
Its contrapositive is ~q → ~p.
If I prosper then I work hard.
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