Sets Exemplar — Class 11 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Sets Exemplar" — 5 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Sets Exemplar" — 5 important questions with detailed answers for CBSE board exam p…

By Syllab.in · Updated Jun 17, 2026

Key Questions Covered:

If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find A ∩ B and A ∪ B.
If U = {1, 2, 3, 4, 5, 6} is universal set and A = {1, 3, 5}, find A'.
Verify De Morgan's law: (A ∪ B)' = A' ∩ B' using A = {1, 2}, B = {2, 3}, U = …
If n(A) = 30, n(B) = 40, n(A ∩ B) = 10, find n(A ∪ B).
In a survey, 50 students like tea, 60 like coffee, 20 like both. How many lik…

Solutions Summary:

Question	Status
If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find A ∩ B and …	✓ Solved
If U = {1, 2, 3, 4, 5, 6} is universal set and A = {1, 3,…	✓ Solved
Verify De Morgan's law: (A ∪ B)' = A' ∩ B' using A = {1, …	✓ Solved
If n(A) = 30, n(B) = 40, n(A ∩ B) = 10, find n(A ∪ B).	✓ Solved
In a survey, 50 students like tea, 60 like coffee, 20 lik…	✓ Solved

Showing 5 of 5 questions

Q1: If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find A ∩ B and A ∪ B.

A ∩ B = {3, 4} (common elements). A ∪ B = {1, 2, 3, 4, 5, 6} (all elements).

Q2: If U = {1, 2, 3, 4, 5, 6} is universal set and A = {1, 3, 5}, find A'.

A' (complement) = U - A = {2, 4, 6}.

Q3: Verify De Morgan's law: (A ∪ B)' = A' ∩ B' using A = {1, 2}, B = {2, 3}, U = {1, 2, 3, 4}.

A ∪ B = {1, 2, 3}. (A ∪ B)' = {4}. A' = {3, 4}, B' = {1, 4}. A' ∩ B' = {4}. LHS = RHS. Verified.

Q4: If n(A) = 30, n(B) = 40, n(A ∩ B) = 10, find n(A ∪ B).

n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 30 + 40 - 10 = 60.

Q5: In a survey, 50 students like tea, 60 like coffee, 20 like both. How many like at least one?

Using inclusion-exclusion: n(Tea ∪ Coffee) = 50 + 60 - 20 = 90 students.

Showing 5 of 5 questions. Visit the full page for complete solutions.