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

CAT Questions | Set theory | De Morgan's Laws

The question is from CAT Set theory. This is about De Morgan's Laws. We need to verify the given statements. 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 2: A´ is defined as the complement of A, as in, set of all elements that are part of the universal set but not in A. How many of the following have to be true?

i. n(A ∪ B)' = n(A' ∩ B')
ii. If A ∩ B=0}, then A' ∪ B'} is equal to the universal set
iii. If A ∪ B = universal set, then A' ∩ B' should be the null set.
iv. If A ⊂ B then A' ∪ B'=(A ∩ B)'

  1. 1
  2. 2
  3. 3
  4. 4

Try 2IIM Online CAT Coaching


Best CAT Online Coaching


Video Explanation


Best CAT Coaching in Chennai


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


Explanatory Answer

Method of solving this CAT Question from Set theory: Do you remember De Morgan´s laws?

Let's look at these statements one at a time:

i. n(A ∪ B)' =n(A' ∩ B')
This is a direct statement of De Morgan´s law. This is definitely true. Just to recap, De Morgan´s laws are as follows:
1. (A ∪ B)' =(A' ∩ B')
2. (A ∩ B)' =(A' ∪ B')

ii. A ∩ B=0, then A' ∪ B' is equal to the universal set
(A ∩ B)' =(A' ∪ B')
If A and B are disjoint sets, A ∩ B=0 and (A ∩ B)' is the universal set. This statement is correct.

iii. If A ∪ B = Universal Set, then A' ∩ B' should be the null set. This means (A ∪ B)' is the null set.

iv. If A ⊂ B, then A' ∪ B'= (A ∩ B)'
If A ⊂ B then A ∩ B=A.
This implies that (A ∩ B)'=A'
If A ⊂ B, then B' ⊂ A' and A' ∪ B'=A'
Thus A' ∪ B'= (A ∩ B)'. This statement is true.

The question is "How many of the following have to be true?"

Hence, the answer is all four statements are true.

Choice D 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