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Write the converse, inverse, contrapositive of the following statement. If a man is bachelor, then he is happy. - Mathematics and Statistics

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Sum

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

If a man is bachelor, then he is happy.

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Solution

Let p : A man is bachelor.
q : A man is happy.

∴ The given statement is p → q.

Its converse is q → p.
If a man is happy then he is bachelor.

Its inverse is ~p → ~q.
If a man is not bachelor then he is not happy.

Its contrapositive is ~q → ~p.
If a man is not happy then he is not bachelor.

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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