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

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Sum

Using the truth table, prove the following logical equivalence.

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)

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Solution

1 2 3 4 5 6 7 8
p q r q∨r p∧(q∨r) p∧q p∧r (p∧q)∨(p∧r)
T T T T T T T T
T T F T T T F T
T F T T T F T T
T F F F F F F F
F T T T F F F F
F T F T F F F F
F F T T F F F F
F F F F F F F F

In the above truth table, the entries in columns 5 and 8 are identical.

∴ p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)

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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