JEE Main 2022 (Online) 26th July Evening ShiftQuestion 1
Let $A=\{1,2,3,4,5,6,7\}$ and $B=\{3,6,7,9\}$. Then the number of elements in the set $\{C\subseteq A:C\cap B\ne\phi\}$ is ________.
Sets, Relations and Function
Answer$112$
Solution
Total subsets of $A$: $2^7=128$. Subsets with $C\cap B=\phi$ must avoid $A\cap B=\{3,6,7\}$: $2^4=16$. Required number $=128-16=112$.