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State true or false:

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

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True

False

answer is B.

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Detailed Solution

We need to check whether every positive integer can be of form

4 q + 2

.
So, it is not possible to write all positive numbers in form

4 q + 2

.
As,

4 q + 2 = 2 (2 q + 1)

.
This means that,

4 q + 2

is an even number.
Therefore, we are unable to express odd numbers in form

4 q + 2

(where q is an integer).
Moreover, since

2 q + 1

is an odd integer, the largest power of 2 that divides

4 q + 1

is 1.
As a result, we are unable to represent the integers in the form of

4 q + 2

.
Therefore, the given statement is false.
The correct statement is every positive integer cannot be of form

4 q + 2

, where

q

is an integer.
Hence, option 2 is correct.

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