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

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Sum

Using the rules in logic, write the negation of the following:

(∼p ∧ q) ∨ (p ∧ ∼q)

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Solution

The negation of (∼p ∧ q) ∨ (p ∧ ∼q) is
∼ [(∼p ∧ q) ∨ (p ∧ ∼q)]
≡ ∼ (p ∧ q) ∧ ∼(p ∧ ∼q) ....(Negation of disjunction)
≡ [∼ (∼p) ∨ ∼q] ∧ [∼p ∨ ∼(∼q)] ........(Negation of conjunction)
≡ (p ∨ ∼q) ∧ (∼p ∨ q) .......(Negation of negation)

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 11.4 | Page 34
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