Relations and F...

Let R = {(P, Q) : OP = OQ , O being the origin} be an equivalence relation on A. The equivalence class [(1, 2)] is

Let a relation T on the set R of real numbers be T = {(a, b) : 1 + ab <0, a, ∈R}. Then from among the ordered pairs (1, 1), (1, 2), (1, -2), (2, 2), the only pair that belongs to T is________.​

For real number x and y, we write  _x R_y ⇔x-y + √2 is an irrational number. Then the relation R is:​

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a  relation on the set A = {1, 2, 3, 4}. The relation  R is

If A = {1, 3, 5, 7} and we define a relation R = {(a, b), a, b ∈A: |a - b| = 8}. Then the number of elements in the relation R is

If A = {1, 3, 5, 7} and define a relation, such that R = {(a, b) a, b  ∈A : |a + b| = 8}. Then how many elements are there in the relation R

In the set N x N, the relation R is defined by (a, b) R (c, d) ⇔ a + d = b + c. Then R is

Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R is ​

Let A = {1, 2, 3, 4, 5, 6, 7}. P = {1, 2}, Q = {3, 7}. Write the elements of the set R so that P, Q and R form a partition that results in equivalence relation.​