Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of each of the following:

(a) an injective mapping from A to B

(b) a mapping from A to B which is not injective

(c) a mapping from B to A.

Given that, A = {2, 3, 4}, B = {2, 5, 6, 7}

(a) an injective mapping from A to B

Let f : A → B denote a mapping f = {(x,y) : y=2x }

Now, y = 2x

When x=2 we get y = 4

Similarly, x=3 and 4 will give y=6 and 8 respectively.

∴ f = {(2,4),(3,6),(4,8)}

We observe that each element of A has unique image in B.

Thus, f is injective.

(b) a mapping from A to B which is not injective

Let g: A → B denote a mapping such that g = {(2,2),(3,5),(4,2)}

We observe that 2 and 4 ∈ A does not have unique image.

Thus, g is not injective.

(c) a mapping from B to A.

Let h : B → A denote a mapping such that

h = {(2,3),(5,2),(6,3),(7,4)}