Question

If $A=\{1,2,3\},B=\{2,4,5\}$ and $C=\{4,1,9\},$ then $A\cap (B\cup C)$= ___.

• A. $(A\cap B)\cup (A\cap C)$
• B. $(A\cup B)\cap (A\cup C)$
• C. $(A\cap B)\cup C$
• D. $\{1,2\}$

Answer 1

Answer: (A), (D)

The correct options are
A $(A\cap B)\cup (A\cap C)$
D $\{1,2\}$

Given $A=\{1,2,3\},B=\{2,4,5\}$ and $C=\{4,1,9\}.$
Then, $A\cap (B\cup C)=\{1,2,3\}\cap \left(\right\{2,4,5\}\cup \{4,1,9\left\}\right)$
$=\{1,2,3\}\cap \{1,2,4,5,9\}$
$=\{1,2\}.$
Also, $(A\cap B)\cup (A\cap C)=\left(\right\{1,2,3\}\cap \{2,4,5\left\}\right)\cup \left(\right\{1,2,3\}\cap \{4,1,9\left\}\right)$
$=\left\{2\right\}\cup \left\{1\right\}$
$=\{1,2\}.$

This property of sets A, B and C such that
$A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$ is called the distributive property of sets (intersection over union).