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Write the negation of p → q

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Question

Write the negation of p → q

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Solution

∼ p → q ≡  (∼p ∨ q)   .......[∵ p → q ≡ ∼p ∨ q]

≡ ∼ (∼p) ∨ ∼ q       .......[De’Morgan’s Law]

≡ ∼ ∼ p ∧ ∼ q

≡  p ∧ ∼ q

≡ p ∧ (∼q)

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Chapter 1.1: Mathematical Logic - Very Short Answers

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Using truth table prove that:

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


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