NDA | Mathematics | Relations

Given the relation  on the set  the minimum number of ordered pair which when added to R make it an equivalence relation is

Let S be the set of all real numbers. then the relation  on S is

Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, the minimum number of ordered pairs which when added to R make it an equivalence relation is

If A and B  are two non-empty sets having n elements in common, then what is the number of common elements in the sets ?

The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then  is given by