Q. 14.1( 285 Votes )

For some integer

Answer :

We know that an integer is said to be even when it is divisible by 2.


Let m be a integer i.e. m = ..., -3, -2, -1, 0, 1, 2, 3, …


Clearly, 'm' may or may not be even, therefore, 'm' can't be an answer.

m + 1 = ..., -2, -1, 0, 1, 2, 3, 4...

Here also, 'm + 1' may or may not be even, therefore, 'm + 1' can't be an answer.

Now, consider 2m i.e. 2m = ...,-6, -4, -2, 0, 2, 4, 6,...

Here, for some integer m, 2m is always integer,

Now, consider 2m + 1, i.e. 2m + 1 = ..., -5, -3, -1, 1, 3, 5, 7,...

Clearly, 2m + 1 is an odd integer, therefore  it can't be an answer


Hence, 2m is only answer.

 

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