Sets — Class 11 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Sets" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Sets" — 8 important questions with detailed answers for CBSE board exam preparatio…
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Key Questions Covered:
- If A = {x : x is a natural number and x < 6} and B = {x : x is an even natura…
- For sets A, B, and C, verify De Morgan's Law: (A ∪ B)' = A' ∩ B' when U = {1,…
- Find the number of subsets and proper subsets of set S = {a, b, c, d}.
- + 5 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| If A = {x : x is a natural number and x < 6} and B = {x :… | ✓ Solved |
| For sets A, B, and C, verify De Morgan's Law: (A ∪ B)' = … | ✓ Solved |
| Find the number of subsets and proper subsets of set S = … | ✓ Solved |
Showing 3 of 8 questions
Q1: If A = {x : x is a natural number and x < 6} and B = {x : x is an even natural number and x ≤ 8}, find A ∪ B and A ∩ B.
Step 1: Write set A in roster form.
A = {1, 2, 3, 4, 5}
Step 2: Write set B in roster form.
B = {2, 4, 6, 8}
Step 3: Find A ∪ B (all elements in either A or B).
A ∪ B = {1, 2, 3, 4, 5, 6, 8}
Step 4: Find A ∩ B (elements common to both A and B).
A ∩ B = {2, 4}
Final Answer: A ∪ B = {1, 2, 3, 4, 5...
Q2: For sets A, B, and C, verify De Morgan's Law: (A ∪ B)' = A' ∩ B' when U = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3}, B = {3, 4, 5}.
Step 1: Find A' and B' with respect to U.
A' = U - A = {4, 5, 6}
B' = U - B = {1, 2, 6}
Step 2: Find A ∪ B.
A ∪ B = {1, 2, 3, 4, 5}
Step 3: Find (A ∪ B)' = U - (A ∪ B).
(A ∪ B)' = {6}
Step 4: Find A' ∩ B'.
A' ∩ B' = {4, 5, 6} ∩ {1, 2, 6} = {6}
Step 5: Verify (A ∪ B)' = A' ∩ B'.
{6} = {6} ✓
Fina...
Q3: Find the number of subsets and proper subsets of set S = {a, b, c, d}.
Step 1: Count the elements in set S.
Number of elements n = 4
Step 2: Find total number of subsets.
Total subsets = 2ⁿ = 2⁴ = 16
Step 3: List some subsets to verify.
∅, {a}, {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c}, {a,b,d}, {a,c,d}, {b,c,d}, {a,b,c,d}
Step 4: Find number ...
Showing 3 of 8 questions. Visit the full page for complete solutions.