Question

Let $A=\left\{1,2,3\right\}$, $B=\left\{3,4\right\}$,$C=\left\{4,5,6\right\}$. Then $A\cup \left(B\cap C\right)$ is

• A. $\left\{3\right\}$
• B. $\left\{1,2,3,4\right\}$
• C. $\left\{1,2,5,6\right\}$
• D. $\left\{1,2,3,4,5,6\right\}$

Answer 1

The correct option is B

$\left\{1,2,3,4\right\}$

Explanation for correct option:

Finding $A\cup \left(B\cap C\right)$ using the given information:

Given, $A=\left\{1,2,3\right\}$

$B=\left\{3,4\right\}$

$C=\left\{4,5,6\right\}$

Let's consider two sets $A$ and $B$ where

$$\begin{gathered} A\cup B=\left\{x:x\in Aorx\in B\right\} \\ A\cap B=\left\{x:x\in Aandx\in B\right\} \end{gathered}$$

Therefore,

$$\begin{gathered} \left(B\cap C\right)=\left\{4\right\} \\ A\cup \left(B\cap C\right)=\left\{1,2,3,4\right\} \end{gathered}$$

Hence, option (B) is the correct answer.