Question

For some integer $\mathrm{m}$, every even integer is of the form

• A. $\mathrm{m}+2$
• B. $2\mathrm{m}$
• C. $2\mathrm{m}-1$
• D. $2\mathrm{m}+1$

Answer 1

The correct option is B

$2\mathrm{m}$

Step 1: Explanation for correct option.

For option B: $2\mathrm{m}$

For $\mathrm{m}=1,2\mathrm{m}=2$, which is even.

For $\mathrm{m}=2,2\mathrm{m}=4$, which is even.

For $\mathrm{m}=3,2\mathrm{m}=6$, which is even.

Thus for some integer $\mathrm{m}=1,2,3,4,...,2\mathrm{m}=2,4,6,8,...$and so on, which are all even.

So, option B is correct

Step 2: Explanation for incorrect option.

For option A: $\mathrm{m}+2$

For $\mathrm{m}=1,\mathrm{m}+2=3$, which is odd.

For $\mathrm{m}=2,\mathrm{m}+2=4$, which is even.

For $\mathrm{m}=3,\mathrm{m}+2=5$, which is odd.

So, option A is incorrect

For option C: $2\mathrm{m}-1$

For $\mathrm{m}=1,2\mathrm{m}-1=1$, which is odd.

For $\mathrm{m}=2,2\mathrm{m}-1=3$, which is odd.

So, option C is incorrect

For option D: $2\mathrm{m}+1$

For $\mathrm{m}=1,2\mathrm{m}+1=3$, which is odd.

For $\mathrm{m}=2,2\mathrm{m}+1=5$, which is odd.

Therefore, for some integer $\mathrm{m}$, every even integer is of the form $2\mathrm{m}$

So, option D is incorrect

Hence, correct option is (B).