CAT Quantitative Aptitude Questions | CAT Set theory Questions - Union and Intersection

The question is from CAT Set theory. It combines functions with set theory. We need to find out the number of onto functions between two sets. CAT exam is known to test on basics rather than high funda ideas. CAT also tests multiple ideas in the same question, and 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023. Set Theory (especially constructing venn diagrams) is a frequently tested topic. Make sure you know the basics from this chapter.

Question 9: Set A = {2, 3, 5, 6, 7}, Set B = {a, b, c}. How many onto functions can be defined from Set B to Set A?

1. 2
2. 3
3. 4
4. None of the above

Explanatory Answer

Method of solving this CAT Question from Set theory: Function question from Set theory which can be solved using Combinatorics?

Number of onto function from Set A to Set B:
There are 3 elements in set B, all these elements need to be mapped to some element in set A.
For a function to exist every element of the domain has a unique value.
a of Set B can be mapped to any of the 5 elements of Set A
b of Set B can be mapped to any of the other 4 elements in Set A and
c of Set B can be mapped to any of the other 3 elements in Set A
Thus the number of onto functions that can be obtained is 5*4*3=60

Number of onto function from Set B to Set A:
There are 5 elements in Set A whereas there are only 3 elements in Set B, which effectively means only 3 elements of Set A at the max can be mapped to Set B.
For a function to exist every element of the domain has a unique value.
Thus no onto function can be defined from set B to Set A

The question is "How many onto functions can be defined from Set B to Set A?"

Hence, the answer is "None of the above.".

Choice D is the correct answer.