Maharashtra State BoardHSC Arts 12th Board Exam
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Determine whether the following statement pattern is a tautology, contradiction or contingency: (p ∧ q) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q) - Mathematics and Statistics

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Sum

Determine whether the following statement pattern is a tautology, contradiction or contingency:

(p ∧ q) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q)

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Solution

p q ∼p ∼q p ∧ q ∼p ∧ q p ∨ ∼q ∼p ∧ ∼q (I) ∨ (II) ∨ (III) ∨ (IV)
        (I) (II) (III) (IV)  
T T F F T F T F T
T F F T F F T F T
F T T F F T F F T
F F T T F F T T T

All the entries in the last column of the above truth table are T.
∴ (p ∧ q) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q) is a tautology.

Concept: Statement Patterns and Logical Equivalence
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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 7.6 | Page 33

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