MHT CET · Maths · Mathematical Reasoning
Let \(\mathrm{p}, \mathrm{q}\) and r be the statements
p : X is an equilateral triangle
\(\mathrm{q}: \mathrm{X}\) is isosceles triangle
\(r: q \vee \sim p\),
then the equivalent statement of \(r\) is
- A If X is not an equilateral triangle, then X is not an isosceles triangle
- B X is neither isosceles nor equilateral triangle
- C X is isosceles but not an equilateral triangle
- D If X is not an isosceles triangle, then X is not an equilateral triangle.
Answer & Solution
Correct Answer
(D) If X is not an isosceles triangle, then X is not an equilateral triangle.
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& q \vee \sim p \\
& \equiv \sim q \rightarrow \sim p \quad \ldots[\because p \rightarrow q \equiv \sim p \vee q]
\end{aligned}\)
\(\therefore \quad\) Option (D) is correct.
& q \vee \sim p \\
& \equiv \sim q \rightarrow \sim p \quad \ldots[\because p \rightarrow q \equiv \sim p \vee q]
\end{aligned}\)
\(\therefore \quad\) Option (D) is correct.
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