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Q.

State true or false:


Every positive integer can be of form 4q+2, where q is an integer.


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a

True

b

False 

answer is B.

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Detailed Solution

We need to check whether every positive integer can be of form 4q+2.
So, it is not possible to write all positive numbers in form 4q+2.
As, 4q+2=2(2q+1).
This means that, 4q+2 is an even number.
Therefore, we are unable to express odd numbers in form 4q+2 (where q is an integer).
Moreover, since 2q+1 is an odd integer, the largest power of 2 that divides 4q+1 is 1.
As a result, we are unable to represent the integers in the form of 4q+2.
Therefore, the given statement is false.
The correct statement is every positive integer cannot be of form 4q+2, where q is an integer.
Hence, option 2 is correct.
 
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