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)] ∧ r - Mathematics and Statistics

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Sum

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

[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r

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Solution

p q r ∼p ∼q p ∨ ∼q ∼p ∧ q (p ∨ ∼q) ∨ (∼p ∧ q) (I) ∧ r
              (I)  
T T T F F T F T T
T T F F F T F T F
T F T F T T F T T
T F F F T T F T F
F T T T F F T T T
F T F T F F T T F
F F T T T T F T T
F F F T T T F T F

The entries in the last column are neither all T nor all F.
∴ [(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r is a contingency.

Concept: Statement Patterns and Logical Equivalence
  Is there an error in this question or solution?

APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 7.7 | Page 33

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