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प्रश्न
Write the converse, inverse, contrapositive of the following statement.
If a man is bachelor, then he is happy.
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उत्तर
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.
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संबंधित प्रश्न
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p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]
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Write the dual statement of the following compound statement.
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~(p ∨ q) → r
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Using the truth table, prove the following logical equivalence.
[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r
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(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
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- `bar(PR)`
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If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].
