Question

identify which of the following relations is a function or is not a function

Answer 1

Step-by-step explanation:

May or may not be. Let R: A→B be a relation from A to B, then R is a subset of AxB = {(a, b) : a€A, b€B}. Then R^(-1) is a relation from B to A . Let us take an example; suppose A = {1, 2, 3} and B = {a, b, c} and R={(1, a),(2, b),(2, c), (3, b)} be a relation from A to B then R^(-1) = {(a, 1),(b, 2),(c, 2), (b, 3)} which is clearly a relation but not a function from B to A, because the element b €B has got two images viz 2 and 3 . But if R = {(1, a),(2, b), (3, c)} then R^(-1) = {(a, 1),(b, 2),(c, 3)} is a function from B to A etc.