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

CAT Questions | Set theory | Union and Intersection

The question is from CAT Set theory. It combines function with set theory. We need to determine type of a function 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 2019. Set Theory (especially constructing venn diagrams) is a frequently tested topic. Make sure you know the basics from this chapter.

Question 12: If set A and set B are bijective and set C and set D are bijective too, State whether there exist a bijection between AC + BD or not

  1. Yes
  2. No
  3. Data insufficient
  4. Cannot be determined

Try 2IIM Online CAT Coaching


Best CAT Online Coaching


Best CAT Coaching in Chennai


Batches filling fast.
Starts Sat, April 27th, 2019


Explanatory Answer

Method of solving this CAT Question from Set theory: How bijective functions are defined?

\\frac{A}{Q}\\) the functions f:A → B and g:C → D are bijections
Then g-1 must exist .
Then for a function h∈ Ac we may define a function T: AC → BBD by T(h) = f ∘ h ∘ g-1 . That is , for d ∈ D, T(h)(d) = f(h(g-1(d)))
Since g-1:D→C, the expression g-1(d) must exist

Now,
As h:C → A and g-1(d) ∈ C then the expression h(g-1(d)) must exist
Again, As h(g-1(d)) ∈ A and f:A → B, the expression f(h(g-1(d))) must exist

Now it only remains to prove that R(h) = f ∘ h ∘ g-1 is a bijection.
To do so, we need to simply provide an inverse.

Now T ∘ R(h) = f ∘ (f-1 ∘ h ∘ g) ∘ g-1
= (f ∘ f-1) ∘ h ∘ (g ∘ g-1 )
= idB ∘ h ∘ idD
= h
Therefore R:h → f-1 ∘ h ∘ g exists and is an inverse to T
Hence there exists a bijection between AC + BD

The question is "If set A and set B are bijective and set C and set D are bijective too, State whether there exist a bijection between AC + BD or not"

Hence, the answer is "Yes".

Choice A is the correct answer.

Best Online CAT Coaching
Learn from 4 time CAT 100 percentiler

Register in 2 easy steps and start learning in 30 seconds!

★ Sign up for Free

Already have an Account?

★ Login to Continue

CAT Coaching in Chennai

Next Weekend Batch Starts Sat, April 27th, 2019

★ CAT Coaching Info

Best CAT Coaching in Chennai
Batches filling fast

Personalised attention, Small batch sizes.

★ Schedule Demo



CAT Online Coaching | CAT Arithmetic Videos On YouTube


Other useful sources for Arithmetic Questions | Set Theory Sample Questions


CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
10-C, Kalinga Colony, Bobbili Raja Salai
K.K.Nagar, Chennai. India. Pin - 600 078

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com