Question

If $A=(5,6,7,8,9),B=\{x:3<x<8\text{and}x\in W\}$ and $C=\{x:x\le 5\text{and}x\in N\}$. Find :

$B\cap C$ and $A\cap (B\cap C)$.

• A. $\{4,5\}$ and $\left\{5\right\}$
• B. $\left\{5\right\}$ and $\left\{5\right\}$
  
• C. $\{3,4,5\}$ and $\{5,6\}$
• D. $\left\{6\right\}$ and $\{3,5,8\}$

Answer 1

The correct option is A $\{4,5\}$ and $\left\{5\right\}$

From the given sets, we have

$B=\{4,5,6,7\}$ as $x$ is greater than $3$, but less than $8$.
And $C=\{1,2,3,4,5\}$ as $x$ is a natural number less than equal to $5$.
Intersection of two sets has the elements common in both the sets.
So, $B\cap C=\{4,5\}$
And, $A\cap (B\cap C)=\{5,6,7,8,9\}\cap \{4,5\}=\left\{5\right\}$