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

Given : $\displaystyle ax + by = d$ and $\displaystyle y= mx + c$.

Find $x$ in terms of $b, c, d$ and $m$.

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 T be the set of all triangles in the Euclidean plane, and let a relation R' on T be defined as aRb if a is congruent to b for all a, b $\in$ T. Then, R is?