The relation $R$ defined on the set of natural numbers as $\{(a, b) : a\}$ differs from $b$ by $\{3\}$,is given by

If $A = \{a, b\}$,$B = \{c, d\}$,$C = \{d, e\}$,then the set $\{(a, c), (a, d), (a, e), (b, c), (b, d), (b, e)\}$ is equal to:

The domain of the function $f(x) = \log_{3 + x}(x^2 - 1)$ is

In a town of $10,000$ families,it was found that $40\%$ of families buy newspaper $A$,$20\%$ buy newspaper $B$,$10\%$ buy newspaper $C$,$5\%$ buy $A$ and $B$,$3\%$ buy $B$ and $C$,and $4\%$ buy $A$ and $C$. If $2\%$ of families buy all three newspapers,then the number of families that buy newspaper $A$ only is:

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

If $f(x) = 4x^3 + 3x^2 + 3x + 4$,then $x^3 f\left( \frac{1}{x} \right)$ is