Consider the following relations on $A = \{1,2,3\}$. $R = \{(1,1), (1,2), (2,1), (2,2), (3,3)\}$, $S = \{(1,1), (1,2), (2,2), (2,3)\}$ and $\Phi = \text{empty set}$. Which one of these forms an equivalence relation?

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

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

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

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

The set of cubes of the natural number is:

The number of integers from $1$ to $100$ which are neither divisible by $3$ nor by $5$ nor by $7$ is