(i) {(1, 2), (2, 3), (3, 4), (2, 1)}

It is not a function because element 2 corresponds to two elements 3 and 1.

(ii) {(a, 0), (b, 0), (c, 1), (d, 1)}

It is a function because under this each element corresponds to one and only one element.

(iii) {(1, a), (2, b), (1, b), (2, a)}

It is not a function because element 1 corresponds to two elements a and b.

(iv) {(a, a), (b, b), (c, c)}

It is a function because first element of ordered pair set is not same.

(v) {a, b}

It is a function because a corresponds to b

(vi) {(4, 1), (4, 2), (4, 3), (4, 4)}

It is not a function because first element of ordered pair set is same.

(vii) {(1, 4), (2, 4), (3, 4), (4, 4)}

It is a function because first element of ordered pair set is unequal.

(viii) {(x, y) : x, y ∈ R, y² = x}

Here y² = x ⇒ y = ±√x and if x = 4 then y = ±2

Hence, element of y is related with 2 and -2 so, it is not a function.

(ix) {(x, y) : x, y ∈ R, x² = y}

It is a function because for y = x², each real value of x there is a unique image in R for each element of R

(x) {(x, y) : x, y ∈ R, x = y³}

It is a function because y = x^1/3, ∀ x ∈ R unique image is the set B.

(xi) {(x, y) : x, y ∈ R, y = x³}

It is also a function because for y = x³ ∀ x ∈ R unique image is in set B.