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

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Sum

Using rules in logic, prove the following:

p ↔ q ≡ ∼(p ∧ ∼q) ∨ ∼(q ∧ ∼p)

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Solution

By the rules of negation of biconditional,
∼ (p ↔ q) ≡ (p ∧ ∼q) ∨ (q ∧ ∼p)
∴ ∼ [(p ∧ ∼q) ∧ (q ∧ ∼p)] ≡ p ↔ q
∴ ∼ (p ∧ ∼q) ∧ ∼ (q ∧ ∼p) ≡ p ↔ q .......(Negation of disjunction)
∴ p ↔ q ≡ ∼(p ∧ ∼q) ∧ ∼(q ∧ ∼p).

Concept: Algebra of Statements
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Balbharati Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 10.1 | Page 34
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