Question

Let $A=\left\{a,b,c\right\}$, $B=\left\{b,c,d\right\}$, $C=\left\{a,b,d,e\right\}$, then $A\cap \left(B\cup C\right)$ is

• A. $\left\{a,b,c\right\}$
• B. $\left\{b,c,d\right\}$
• C. $\left\{a,b,d,e\right\}$
• D. $\left\{e\right\}$

Answer 1

The correct option is A

$\left\{a,b,c\right\}$

Explanation for the correct answer:

Finding $A\cap \left(B\cup C\right)$:

The union of two sets $A$and $B$ is the set of all elements which are either in $A$ or in $B$. It is denoted by $A\cup B$.

$A\cup B=\left\{x:x\in A\text{or}x\in B\right\}$.

The intersection of two sets $A$and $B$ is the set of all elements common to both $A$ and $B$. It is denoted by $A\cap B$.

$A\cap B=\left\{x:x\in A\text{and}x\in B\right\}$

Given,

$A=\left\{a,b,c\right\}$,

$B=\left\{b,c,d\right\}$

$C=\left\{a,b,d,e\right\}$

$$\begin{gathered} \Rightarrow \left(B\cup C\right)=\left\{a,b,c,d,e\right\}\left[\text{Elements in}BorC\right] \\ \Rightarrow A\cap \left(B\cup C\right)=\left\{a,b,c\right\}\left[\text{Common in set}A\text{and}B\cup C\right] \end{gathered}$$

Hence, option (A) is the correct answer.