Let $\mathrm{p}, \mathrm{q}$ and r be the statements p : X is an equilateral triangle $\mathrm{q}:…

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
  1. If X is not an equilateral triangle, then X is not an isosceles triangle
  2. X is neither isosceles nor equilateral triangle
  3. X is isosceles but not an equilateral triangle
  4. If X is not an isosceles triangle, then X is not an equilateral triangle.

Solution

$\begin{aligned} & q \vee \sim p \\ & \equiv \sim q \rightarrow \sim p \quad \ldots[\because p \rightarrow q \equiv \sim p \vee q] \end{aligned}$ $\therefore \quad$ Option (D) is correct.

Asked in: MHT CET 2024 (11 May Shift 1)

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