Step-by-step Answer
PAGE: 626SET: ExercisesPROBLEM: 37
Please look in your text book for this problem Statement

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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