If $\displaystyle f(x) = \frac{x+1}{x-1}$, find $\displaystyle f^{-1}(x)$.

Let $\displaystyle A = \{a, b, c, d, e\}$ then the number of proper subsets is

The numbers of proper subset of the set $\displaystyle (3, 4, 5, 6, 7)$ is

If $\displaystyle A = (1, 2, 3, 4, 5, 6, 7)$ and $\displaystyle B = (2, 4, 6, 8)$. Cardinal number of $\displaystyle A - B$ is:

$\displaystyle (A^c)^c = ?$ Note: This que is from matrix (deleted topic).

Two finite sets respectively have $\displaystyle x$ and $\displaystyle y$ number of elements. The total number of subsets of the first is $\displaystyle 56$ more than the total number of subsets of the second. The value of $\displaystyle x$ and $\displaystyle y$ respectively.

The set of cubes of the natural number is: