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
≡ (p ∧ ∼p) ∨ (q ∧ ∼p) .....(Distributive Law)
≡ F ∨ (q ∧ ∼p) ...........(Complement Law)
≡ q ∧ ∼p ...........(Identity Law)
≡ ∼p ∧ q .............(Commutative 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 10.2 | Page 34
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