Question

If $A=\{1,2\},$ $B=\{3,4\}$ and $C=\{5,6\},$ then $A\cup (B\cup C)$ = ___.

• A. $(A\cup B)\cup C$
• B. $\{1,2,3,4,5,6\}$
• C. $(A\cap B)\cap C$
• D. $A\cap (B\cap C)$

Answer 1

Answer: (A), (B)

The correct options are
A $(A\cup B)\cup C$
B $\{1,2,3,4,5,6\}$

Given $A=\{1,2\},$ $B=\{3,4\}$ and $C=\{5,6\}.$
$A\cup (B\cup C)=\{1,2\}\cup \left(\right\{3,4\}\cup \{5,6\left\}\right)=\{1,2\}\cup \{3,4,5,6\}=\{1,2,3,4,5,6\}$
Also, $(A\cup B)\cup C=\left(\right\{1,2\}\cup \{3,4\left\}\right)\cup \{5,6\}=\{1,2,3,4\}\cup \{5,6\}=\{1,2,3,4,5,6\}.$

Note that $(A\cup B)\cup C=A\cup (B\cup C)$ is known as the associative property of union of sets.