Question

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

• A. $\{3,4,6\}$
• B. $\{1,2,3\}$
• C. $\{1,4,3\}$
• D. None of these

Answer 1

The correct option is A

$\{3,4,6\}$

Explanation for the correct option:

Finding set of common element:

Given,

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

Then,

$$\begin{gathered} (A\cup B)=\{1,2,3,4,5,6\} \\ \mathbf{(}\mathit{A}\mathbf{\cup }\mathit{B}\mathbf{)}\mathbf{\cap }\mathit{C}\mathbf{}\mathbf{=}\mathbf{\{}\mathbf{3}\mathbf{,}\mathbf{}\mathbf{4}\mathbf{,}\mathbf{}\mathbf{6}\mathbf{\}} \end{gathered}$$

[$\because \left(A\cup B\right)$ is defined as the set that consists of all elements belonging to either set $A$ or set $B$ or both and $\left(A\cap B\right)$ is defined of all elements that belongs to both $A$ and $B$]

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