Question

Let A={1,2,3} and B={4,5,6}. Which one of the following functions is bijective?

(a) f={(2,4),(2,5),(2,6)}

(b) f={(1,5),(2,4),(3,4)}

(c) f={(1,4),(1,5),(1,6)}

(d) f={(1,4),(2,5),(3,6)}

I had been asked this question during an interview.

Question is taken from Types of Functions topic in chapter Relations and Functions of Mathematics – Class 12

Answer 1

Right option is (d) f={(1,4),(2,5),(3,6)}

The explanation is: f={(1,4),(2,5),(3,6)} is a bijective function.

One-one: It is a one-one function because every element in set A={1,2,3} has a distinct image in set B={4,5,6}.

Onto: It is an onto function as every element in set B={4,5,6} is the image of some element in set A={1,2,3}.

f={(2,4),(2,5),(2,6)} and f={(1,4),(1,5),(1,6)} are many-one onto.

f={(1,5),(2,4),(3,4)} is neither one – one nor onto.