Question

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

• A. $(A\cup B)\cap (A\cup C)$
• B. $(A\cap B)\cup (A\cap C)$
• C. $\{1,2,3,4\}$
• D. $(A\cup B)\cap C$

Answer 1

Answer: (A), (C)

The correct options are
A $(A\cup B)\cap (A\cup C)$
C $\{1,2,3,4\}$

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

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