Question

If $A=\{2,3,4,8,10\},B=(3,4,5,10,12\},C=\{4,5,6,12,14\}$, then $(A\cap B)\cup (A\cap C)$ is equal to

• A. $\{3,4,10\}$
• B. $\{2,9,10\}$
• C. $\{4,5,6\}$
• D. $\{3,5,14\}$

Answer 1

Answer: (A)

$\{3,4,10\}$

$A=\{2,3,4,8,10\},B=\{3,4,5,10,12\},C=\{4,5,6,12,14\}$

To find : $(A\cap B)$ $\cup (A\cap C)$

$A\cap B$ = elements common in sets $A$ and $B$ $⟹A\cap B=\{3,4,10\}$

$A\cap C$ = elements common in sets $A$ and $C$ $⟹A\cap C=\left\{4\right\}$

Now,

$(A\cap B)\cup (A\cap C)=$elements in $(A\cap B)$ and $(A\cap C)$

$(A\cap B)\cup (A\cap C)=\{3,4,10\}\cup \left\{4\right\}$

$(A\cap B)\cup (A\cap C)=\{3,4,10\}$.