Let A = {0, 1} and N be the set of natural numbers. Then the mapping f :N → A defined by f (2n–1) = 0, f (2n) = 1,∀n ∈N, is onto.

Question

State True or False for the statement:

Let A = {0, 1} and N be the set of natural numbers. Then the mapping f :N → A defined by f (2n–1) = 0, f (2n) = 1,∀n ∈N, is onto.

Answer 1

True

Given that, f :N → A defined by f (2n–1) = 0, f (2n) = 1,∀n ∈N,

We observe that for each element of A(co-domain) there exist a pre image in N(domain).

For 0 ∈ A there exist (2n-1),∀ n ∈N

For 1 ∈ A there exist (2n),∀ n ∈N

Thus, the mapping is onto.