If A = {1, 2, 3, 4), B = {1, 2, 3, 4, 5, 6} are two sets and the funct

1.	If A = {1, 2, 3, 4), B = {1, 2, 3, 4, 5, 6} are two sets and the function f : A → B is defined by f (x) = x + 2 ∀ x ∈ A, then the function f is(a) bijective (b) one-one (c) onto (d) many-one
Answer» Answer: (b) = one - one f (x) = x + 2 and f : A → B ∴ f (1) = 1 + 2 = 3, f (2) = 2 + 2 = 4 f (3) = 3 + 2 = 5, f (4) = 4 + 2 = 6 Thus each element in A has a unique image in B and no two elements in B have the same pre-image in A. So f is one-one. But not all the elements of B, i.e., 1 and 2 have a pre-image in A. So, the function f is not onto

If A = {1, 2, 3, 4), B = {1, 2, 3, 4, 5, 6} are two sets and the function f : A → B is defined by f (x) = x + 2 ∀ x ∈ A, then the function f is(a) bijective (b) one-one (c) onto (d) many-one

Answer»

Answer: (b) = one - one

f (x) = x + 2 and f : A → B

∴ f (1) = 1 + 2 = 3, f (2) = 2 + 2 = 4

f (3) = 3 + 2 = 5, f (4) = 4 + 2 = 6

Thus each element in A has a unique image in B and no two elements in B have the same pre-image in A.

So f is one-one.

But not all the elements of B, i.e., 1 and 2 have a pre-image in A.

So, the function f is not onto