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Statement : is divisible by .
The statement is False.
Proof :
Let be the statement is divisible by .
is the statement that is divisible by , is true since
which is divisible by .
Assume is true where is a positive integer and we have to prove that must be
true i.e., show that for some integer implies that is divisible by .
Plug in differerent values :
For :
which is not divisible by but divisible by .
For :
which is divisible by .
For :
which is not divisible by but divisible by .
Therefore, is divisible by only when is an odd number.
The expression is not divisible by .
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