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Write the converse, inverse, and contrapositive of the following statement. If he studies, then he will go to college. - Mathematics and Statistics

Sum

Write the converse, inverse, and contrapositive of the following statement.

If he studies, then he will go to college.

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Solution

Let p : He studies.
q : He will go to college.

∴ The given statement is p → q.

Its converse is q → p.
If he will go to college then he studies.

Its inverse is ~p → ~q.
If he does not study then he will not go to college.

Its contrapositive is ~q → ~p.
If he will not go to college then he does not study.

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