Find the cardinal number of the following set $\{x: x\}$ is a natural number $\leq 30$ and is divisible by $7$ or $\{11\}$

If $A = \{ x : x^2 - 5x + 6 = 0 \}, B = \{ 2, 4 \}, C = \{ 4, 5 \}$,then $A \times (B \cap C)$ is

Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$, then

Given $n(U) = 20$,$n(A) = 12$,$n(B) = 9$,$n(A \cap B) = 4$,where $U$ is the universal set,$A$ and $B$ are subsets of $U$,then $n((A \cup B)^C) = $

Which of the following statements is false (where $A$ and $B$ are two non-empty sets)?

Out of $100$ families in the neighbourhood,$50$ have radios,$75$ have $TVs$ and $25$ have $VCRs$. Only $10$ families have all three and each $VCR$ owner also has a $TV$. If some families have radio only,how many have only $TV$?