$\"\"$

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Statement : $\"\"$ is divisible by $\"\"$ .

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The statement is False.

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Proof :

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Let $\"\"$ be the statement $\"\"$ is divisible by $\"\"$ .

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$\"\"$ is the statement that $\"\"$ is divisible by $\"\"$ , $\"\"$ is true since $\"\"$

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which is divisible by $\"\"$ .

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Assume $\"\"$ is true where $\"\"$ is a positive integer and we have to prove that $\"\"$ must be

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true i.e., show that $\"\"$ for some integer $\"\"$ implies that $\"\"$ is divisible by $\"\"$ .

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Plug in differerent values :

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For $\"\"$ :

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$\"\"$ which is not divisible by $\"\"$ but divisible by $\"\"$ .

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For $\"\"$ :

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$\"\"$ which is divisible by $\"\"$ .

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For $\"\"$ :

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$\"\"$ which is not divisible by $\"\"$ but divisible by $\"\"$ .

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Therefore, $\"\"$ is divisible by $\"\"$ only when $\"\"$ is an odd number.

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$\"\"$

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The expression $\"\"$ is not divisible by $\"\"$ .