Maharashtra State BoardHSC Arts 12th Board Exam
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Examine whether the following statement pattern is a tautology or a contradiction or a contingency. [(p → q) ∧ ∼ q] → p - Mathematics and Statistics

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Sum

Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

[(p → q) ∧ ∼ q] → ∼ p

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Solution

p q ∼ p ∼ q p → q (p → q) ∧ ∼ q [(p → q) ∧ ∼ q] → ∼ p
T T F F T F T
T F F T F F T
F T T F T F T
F F T T T T T

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

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 7.1 | Page 33

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