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Let N be the set of natural numbers and ...

Let N be the set of natural numbers and f : N->N be a function given by f(x)=x+1 for `x in N`.Which one of the following is correct? a. f is one-one and onto b. f is one-one but not onto c. f is only onto d. f is neither one-one nor onto

A

f is one-one and onto

B

f is one-one but not onto

C

f is only onto

D

f is neither one-one nor onto

Text Solution

Verified by Experts

The correct Answer is:
B
To show f is one-one.
Let `f(x)=f(y)("To show: x=y")`
`impliesx+1=y+1`
`impliesx=y`
Hence, f is one-one,
Now, 'f' is not onto because every element of codomain does not have it' s pre-image in domain.
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