$\mathrm{S}_1:$ If -7 is an integer, the $\sqrt{-7}$ is a complex number $\mathrm{S}_2:-7$ is not an integer…

$\mathrm{S}_1:$ If -7 is an integer, the $\sqrt{-7}$ is a complex number $\mathrm{S}_2:-7$ is not an integer or $\sqrt{-7}$ is a complex number
  1. $\mathrm{S}_1$ and $\mathrm{S}_2$ are converse statements of each other
  2. $S_1$ and $S_2$ are negations of each other
  3. $\mathrm{S}_1$ and $\mathrm{S}_2$ are equivalent statements
  4. $S_1$ and $S_2$ are contrapositive of each other

Solution

Let $p:-7$ is an integer. $\mathrm{q}: \sqrt{-7}$ is a complex number. Logical form of $\mathrm{S}_1 \equiv \mathrm{p} \rightarrow \mathrm{q}$ Logical form of $\mathrm{S}_2 \equiv \sim \mathrm{p} \vee \mathrm{q}$ We know that $\mathrm{p} \rightarrow \mathrm{q} \equiv \sim \mathrm{p} \vee \mathrm{q}$ $\therefore \mathrm{S}_1$ and $\mathrm{S}_2$ are equivalent statements.

Asked in: MHT CET 2021 (23 Sep Shift 2)

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