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State the dual of the following statement by applying the principle of duality. (p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q) - Mathematics and Statistics

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प्रश्न

State the dual of the following statement by applying the principle of duality.

(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)

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उत्तर

(p ∨ ~q) ∧ (~ p ∨ q) ≡ (p ∧ q) ∨ ~(p ∨ q)

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अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.16 | पृष्ठ ३३

संबंधित प्रश्न

Write the dual of the following statements: (p ∨ q) ∧ T


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By constructing the truth table, determine whether the following statement pattern ls a tautology , contradiction or . contingency.  (p →  q) ∧  (p ∧ ~ q ).


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Using the truth table prove the following logical equivalence.

p → (q ∧ r) ≡ (p → q) ∧ (p → r)


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Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

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Prove that the following statement pattern is a tautology.

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(p∧~q) → (~p∧~q)


Using the truth table, verify

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Karina is very good or everybody likes her.


Write the dual statement of the following compound statement.

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With proper justification, state the negation of the following.

(p → q) ∧ r


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[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r


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[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)


The converse of contrapositive of ∼p → q is ______.


If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].


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