Question

Given the sets $A=\left\{1,2,3\right\},B=\left\{3,4\right\},C=\left\{4,5,6\right\}$ then $A\cup (B\cap C)$ is

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

Answer 1

The correct option is B

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

Explanation for correct option:

Finding the value of $\mathit{A}\mathbf{}\mathbf{\cup }\mathbf{}\mathbf{(}\mathit{B}\mathbf{}\mathbf{\cap }\mathbf{}\mathit{C}\mathbf{)}$:

Given, $A=\left\{1,2,3\right\},B=\left\{3,4\right\},C=\left\{4,5,6\right\}$

Now,

$\begin{array}{rcl}(B\cap C)& =& \{3,4\}\cap \{4,5,6\}\\ \mathbf{}& \mathbf{=}& \mathbf{\left\{}\mathbf{4}\mathbf{\right\}}\end{array}$

Also,

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

$\mathbf{\therefore }\mathit{A}\mathbf{\cup }\mathbf{(}\mathbf{B}\mathbf{\cap }\mathbf{C}\mathbf{)}\mathbf{=}\mathbf{\{}\mathbf{1}\mathbf{,}\mathbf{2}\mathbf{,}\mathbf{3}\mathbf{,}\mathbf{4}\mathbf{\}}$

Hence, option(B) is correct.