Maharashtra State BoardHSC Arts 12th Board Exam
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Using the rule of negation write the negation of the following with justification. ∼ (p ∧ q) ∨ (p ∨ ∼ q) - Mathematics and Statistics

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Sum

Using the rule of negation write the negation of the following with justification.

∼ (p ∧ q) ∨ (p ∨ ∼ q)

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Solution

The negation of ∼ (p ∧ q) ∨ (p ∨ ∼ q) is
∼ [∼ (p ∧ q) ∨ (p ∨ ∼ q)] ≡ ∼ [∼ (p ∧ q)] ∧ ∼ (p ∨ ∼ q) ...........(Negation of disjunction)
≡ ∼ [∼ (p ∧ q)] ∧ [∼ p ∧ ∼ (∼ q)] .........(Negation of disjunction)
≡ (p ∧ q) ∧ (∼ p ∧ q) ...........(Negation of negation)

Concept: Negations of Compound Statements
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