Sets Relations And Functions Question 56
Question: If $ A={4n+2|n $ is a natural number} and $ B={3n|n $ is a natural number,}, then what is $ (A\cap B) $ equal to?
Options:
A) $ {12n^{2}+6n|n $ is a natural number}
B) $ {24n-12|n $ is a natural number}
C) $ {60n+30|n $ is a natural number}
D) $ {12n-6|n $ is a natural number}
Show Answer
Answer:
Correct Answer: D
Solution:
- [d]Let $ A={4n+2:n\in N} $ and $ B={3n:n\in N} $
$ \Rightarrow A={6,10,14,18,22,26,30,34,38,42…} $ And $ B={3,6,9,12,15,18,21,24,27,30…} $
$ \therefore A\cap B={6,18,30,42…} $ $ =6+12n-12=12n-6. $ Hence, $ A\cap B={12n-6:n $ is a natural number}.
BETA
