Q. 13

Let f:N <span lan

Answer :

Given: f (n) = (n + 1)/ 2, if n is odd

n/ 2, if n is even

Case 1: When n is odd,

When n = 1,

When n = 3,

When n = 2k – 1, … (1)

Case 2: When n is even,

When n = 2,

When n = 4,

When n = 2k, … (2)

When n = 2n, … (3)

From (1) and (2),

f (2k – 1) = f (2k)

f is not one – one.

From (3),

f (2n) = n

f is onto.

f is onto but not one – one.

Hence f is not bijective.

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