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Question Bank [2022] — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Question Bank [2022]1 Mark
MCQ
The false statement in the following is ______.
  • A
    $p \wedge(\sim p)$ is contradiction
  • ✓
    $( p \rightarrow q ) \leftrightarrow(\sim q \rightarrow \sim p )$ is a contradiction
  • C
    $\sim(\sim p) \leftrightarrow p$ is a tautology
  • D
    $p \vee(\sim p) \leftrightarrow p$ is a tautology
✓

Answer

Correct option: B.
$( p \rightarrow q ) \leftrightarrow(\sim q \rightarrow \sim p )$ is a contradiction
The false statement in the following is (p → q) ↔ (∼ q → ∼ p) is a contradiction.

Explanation:

(p → q) ↔ (∼ q → ∼ p)

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

In the above table, all the entries in the last column are T. Therefore, the given statement pattern is a tautology.

∴ The false statement is (p → q) ↔ (∼ q → ∼ p) is a contradiction.

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