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$\mathrm{S}_1:$ 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
Options:
$\mathrm{S}_2:-7$ is not an integer or $\sqrt{-7}$ is a complex number
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Verified Answer
The correct answer is:
$\mathrm{S}_1$ and $\mathrm{S}_2$ are equivalent statements
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.
$\mathrm{q}: \sqrt{-7}$ 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.
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