Sets Relations And Functions Question 12
Question: Let n denote the set of natural numbers and $ A=\{n^{2}:n\in N\} $ and $ B=\{n^{3}:n\in N\}, $ which one of the following is incorrect?
Options:
A) $ A\cup B=N $
B) The complement of $ (A\cup B) $ is an infinite set
C) $ A\cap B $ Must be a finite set
D) $ A\cap B $ Must be proper subset of $ \{m^{6}:m\in N\} $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a]Let $ A=\{n^{2}:n\in N\} $ and $ B=\{n^{3}:n\in N\} $ $ A=\{1,4,9,16,….\} $ And $ B=\{1,8,27,64,…\} $ Now, $ A\cap B=\{1\} $ which is a finite set. Also, $ A\cup B=\{1,4,8,9,27…..\} $ So, complement of $ A\cup B $ is infinite set. Hence, $ A\cup B\ne N $
BETA
