Let A = 1,2,3,4,5,6,7 and B = 3,6,7,9.

Question

Let $A = \{1,2,3,4,5,6,7\}$ and $B = \{3,6,7,9\}$. Then the number of elements in the set $\{C\subseteq A : C\cap B
eq\emptyset\}$ is \_\_\_\_.

Answer: 112

Accepted Answer

Relevant elements of $B$ inside $A$: $\{3,6,7\}$ (9 is not in $A$).

Total subsets of $A$: $2^7=128$. Subsets with $C\cap B=\emptyset$ must avoid $3,6,7$, i.e. $C\subseteq\{1,2,4,5\}$: $2^4=16$ such subsets.

$128-16 = 112$

Solutions · 1