Question

Let P={10,20,30} and Q={5,10,15,20}. Which one of the following functions is one – one and not onto?

(a) f={(10,5),(10,10),(10,15),(10,20)}

(b) f={(10,5),(20,10),(30,15)}

(c) f={(20,5),(20,10),(30,10)}

(d) f={(10,5),(10,10),(20,15),(30,20)}

I got this question during a job interview.

Origin of the question is Types of Functions in chapter Relations and Functions of Mathematics – Class 12

Answer 1

Right answer is (b) f={(10,5),(20,10),(30,15)}

The best I can explain: The function f={(10,5),(20,10),(30,15)} is one -one and not onto. The function is one-one because element is set P={10,20,30} has a distinct image in set Q={5,10,15,20}. The function is not onto because every element in set Q={5,10,15,20} does not have a pre-image in set P={10,20,30} (20 does not have a pre-image in set P).

f={(10,5),(10,10),(10,15),(10,20)} and f={(10,5),(10,10),(20,15),(30,20)} are many – one onto.

f={(20,5),(20,10),(30,10)} is neither one – one nor onto.