Sets-Relations-And-Functions Question 135
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
