UGC NET CSE | June 2023 | Part 2: 62

Question

If $A=\{4 n+2 \mid n$ is a natural number $\}$ and $B=\{3 n \mid n$ is a natural number $\}$. Which of the following is correct for $A \cap B$ ?

• A. $\left\{12 n^{2}+6 n \mid n\right.$ is a natural number $\}$
• B. $\{24 \mathrm{n}-12 \mid \mathrm{n}$ is a natural number $\}$
• C. $\{60 \mathrm{n}+30 \mid \mathrm{n}$ is a natural number $\}$
• D. $\{12 \mathrm{n}-6 \mid \mathrm{n}$ is a natural number $\}$

 

Answer 1

It is given that:

• $A=4n+2,n $ is natural numbers, so set $A=(6,10,14,18,22,26,34,38,42,46….\infty)$
• $B=3n,n$ is natural number ,so $B=(3,6,8,12,15,18,21,24,27,30,33,36….\infty)$
• $\therefore A \cap B=6,18,30,42...\infty\implies (12n-6)$ where  $n$ is natural number.

Option $(D)$ is correct.