Question

Let M={5,6,7,8} and N={3,4,9,10}. Which one of the following functions is neither one-one nor onto?

(a) f={(5,3),(5,4),(6,4),(8,9)}

(b) f={(5,3),(6,4),(7,9),(8,10)}

(c) f={(5,4),(5,9),(6,3),(7,10),(8,10)}

(d) f={(6,4),(7,3),(7,9),(8,10)}

This question was addressed to me during an interview for a job.

This question is from Types of Functions in section Relations and Functions of Mathematics – Class 12

Answer 1

Right choice is (a) f={(5,3),(5,4),(6,4),(8,9)}

The explanation: The function f={(5,3),(5,4),(6,4),(8,9)} is neither one -one nor onto.

The function is not one – one 8 does not have an image in the codomain N and we know that a function can only be one – one if every element in the set M has an image in the codomain N.

A function can be onto only if each element in the co-domain has a pre-image in the domain X. In the function f={(5,3),(5,4),(6,4),(8,9)}, 10 in the co-domain N does not have a pre- image in the domain X.

f={(5,3),(6,4),(7,9),(8,10)} is both one-one and onto.

f={(5,4),(5,9),(6,3),(7,10),(8,10)}  and f={(6,4),(7,3),(7,9),(8,10)} are many – one onto.