Maharashtra State BoardHSC Commerce 12th Board Exam
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Using the truth table, prove the following logical equivalence. ~p ∧ q ≡ [(p ∨ q)] ∧ ~p - Mathematics and Statistics

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Sum

Using the truth table, prove the following logical equivalence.

~p ∧ q ≡ [(p ∨ q)] ∧ ~p

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Solution

1 2 3 4 5 6
p q ~p ~p∧q (p∨q) (p∨q)∧~p
T T F F T F
T F F F T F
F T T T T T
F F T F F F

In the above truth table, the entries in columns 4 and 6 are identical.

∴ ~p ∧ q ≡ [(p ∨ q)] ∧ ~p

Concept: Statement Patterns and Logical Equivalence
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.14 | Page 33
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