Maharashtra State BoardHSC Arts 12th Board Exam
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Without using truth table prove that: (p ∨ q) ∧ (p ∨ ∼ q) ≡ p - Mathematics and Statistics

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Sum

Without using truth table prove that:

(p ∨ q) ∧ (p ∨ ∼ q) ≡ p

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Solution

L.H.S. = (p ∨ q) ∧ (p ∨ ∼ q)

≡ p ∨ (q ∧ ∼ q) ..........(Distributive Law)

≡ p ∨ F .........(Complement Law)

≡ p .........(Identity Law)

= R.H.S.

Concept: Algebra of Statements
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