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) - Mathematics and Statistics

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Sum

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

(p → q) ∧ (p ∧ ∼q)

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Solution

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

All the entries in the last column of the above truth table are F.
∴ (p → q) ∧ (p ∧ ∼q) is a contradiction.

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 7.3 | Page 33

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