Maharashtra State BoardHSC Commerce 12th Board Exam
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Write the converse, inverse, contrapositive of the following statement. If I do not work hard, then I do not prosper. - Mathematics and Statistics

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Sum

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

If I do not work hard, then I do not prosper.

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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.

Concept: Statement Patterns and Logical Equivalence
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.15 | Page 33
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