$A$ survey shows that $63\%$ of the Americans like cheese whereas $76\%$ like apples. If $x\%$ of the Americans like both cheese and apples,then

Let $P(n) : 3^n < n!$ for $n \in N$. If this statement is true for all $n \geq \lambda$,then the smallest value of $\lambda$ is:

Each set $X_r$ contains $5$ elements and each set $Y_r$ contains $4$ elements and $\bigcup_{r = 1}^{24} X_r = S = \bigcup_{r = 1}^n Y_r$. If each element of set $S$ belongs to exactly $10$ of the $X_r$'s and to exactly $6$ of the $Y_r$'s,then $n$ is equal to:

If $n(U) = 600$,$n(A) = 100$,$n(B) = 200$,and $n(A \cap B) = 50$,then $n(\bar{A} \cap \bar{B})$ is (where $U$ is the universal set and $A$ and $B$ are subsets of $U$).

The shaded region in the Venn diagram can be represented by which of the following?

If $A$ and $B$ are sets,then $A \cap (B - A)$ is