Question

If $A=\{1,2,3\}$, $B=\{3,4\}$ and $C=\{4,5,6\}$, then $A\cup (B\cap C)$ is equal to

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

Answer 1

The correct option is D

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

Step1. Finding intersection of the set.

$A=\{1,2,3\}$

$B=\{3,4\}$

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

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

Step2. Finding union of set.

Now,

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

Hence, correct option is $\mathbf{\left(}\mathit{D}\mathbf{\right)}$