Question

The number of unordered pairs $(A,B)$, of subsets of the set $S=\{1,2,....,10\}$, such that $A\cap B=\varnothing$ and $A\cup B=S$, is

• A. $2^{10}$
• B. $2^9$
• C. ${}^{10}{C}_2$
• D. $1+2^5$

Answer 1

Answer: (A)

$2^{10}$

No. of ordered pairs${=}^{10}{C}_0{+}^{10}{C}_1+....{+}^{10}{C}_{10}=2^{10}$