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Using the rule of negation write the negation of the following with justification. p → (p ∨ ∼ q) - Mathematics and Statistics

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प्रश्न

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

p → (p ∨ ∼ q)

योग

उत्तर

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

≡ p ∧ [∼ p ∧ ∼ (∼ q)] .....(Negation of disjunction)

≡ p ∧ (∼ p ∧ q) .......(Negation of negation)

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Negations of Compound Statements
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अध्याय 1: Mathematical Logic - Exercise 1.4 [पृष्ठ २१]

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