Maharashtra State BoardHSC Arts 12th Board Exam
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Using rules in logic, prove the following: ∼ (p ∨ q) ∨ (∼p ∧ q) ≡ ∼p - Mathematics and Statistics

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Sum

Using rules in logic, prove the following:

∼ (p ∨ q) ∨ (∼p ∧ q) ≡ ∼p

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Solution

∼ (p ∨ q) ∨ (∼p ∧ q)
≡ (∼p ∧ ∼q) ∨ (∼p ∧ q) ..........(Negation of disjunction)
≡ ∼p ∧ (∼q ∨ q) ........(Distributive Law)
≡ ∼p ∧ T ............(Complement Law)
≡ ∼p ............(Identity Law)
∴ ∼ (p ∨ q) ∨ (∼p ∧ q) ≡ ∼p

Concept: Algebra of Statements
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 10.3 | Page 34
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