Question

Let $A=\left\{a,b,d,e\right\}$;$B=\left\{c,d,f,m\right\}$;$C=\left\{a,l,m,o\right\}$ then $C\cap \left(A\cup B\right)$ will be given by

• A. $\left\{a,d,l,m\right\}$
• B. $\left\{b,c,l,o\right\}$
• C. $\left\{a,m\right\}$
• D. $\left\{a,b,c,d,f,l,m,o\right\}$

Answer 1

The correct option is C

$\left\{a,m\right\}$

Determine $C\cap \left(A\cup B\right)$.

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 $A\cap B$.

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

We have, $A=\left\{a,b,d,e\right\}$, $B=\left\{c,d,f,m\right\}$, $C=\left\{a,l,m,o\right\}$

$$\begin{gathered} \therefore \left(A\cup B\right)=\{a,b,d,e\}\cup \{c,d,f,m\} \\ =\left\{a,b,c,d,e,f,m\right\}\left[\text{either in set}A\text{or}B\right] \end{gathered}$$

again for $C\cap \left(A\cup B\right)$

$$\begin{gathered} C\cap \left(A\cup B\right)=\{a,i,m,o\}\cap \{a,b,c,d,e,f,m\} \\ =\left\{a,m\right\}\left[\text{common in set}CandA\cup B\right] \end{gathered}$$

Hence, option (C) is the correct answer.