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 $TV$?

In which of the following cases,$A=B$?

$A$ and $B$ are two subsets of set $S = \{1, 2, 3, 4\}$ such that $A \cup B = S$. Find the number of ordered pairs $(A, B)$.

If $A = \{ 2, 4, 5 \}$ and $B = \{ 7, 8, 9 \}$,then $n(A \times B)$ is equal to

If $n(A) = 4$,$n(B) = 3$,and $n(A \times B \times C) = 24$,then $n(C) = $

In a class of $100$ students, the number of students who passed in English only is $46$, in Maths only is $46$, and in Commerce only is $58$. The number of students who passed in English and Maths is $16$, in Maths and Commerce is $24$, and in English and Commerce is $26$. The number of students who passed in all three subjects is $7$. Find the number of students who failed in all the subjects.