Total number of equivalence relations defined in the set $S=\left\{a, b, c\right\}$ is?

Let $\displaystyle R = \{(x, x + 5) : x \in \{0,1, 2, 3, 4, 5\} \}$

Find dom $\displaystyle (R)$ and range $\displaystyle (R)$. And enter the common element between them.

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set $A \times B$, each having at least three elements is............

If $A = \{ 1,2,3,4,5,6 \} , B = \{ 1,2 \} ,$ then $\frac { A } { \left( \frac { A } { B } \right) }$ equal to 

The number of subsets $R\,of\,P\, = \left\{ {1,2,3,....8} \right\}$ which satisfies the property 'There exist integers $a < \,b < \,c$ with $a\, \in \,R,b\, \notin \,R,c\, \in \,R''\,$ is