Sets — Class 11 Mathematics
Core Concepts
A set is a well-defined collection of distinct objects. Sets may be written in roster form, set-builder form or described in words. If A={1,2,3}, then 2∈A, while 5∉A.
Worked Examples
Example 1: If A={1,2,3,4} and B={3,4,5,6}, then A∪B={1,2,3,4,5,6}, A∩B={3,4}, and A−B={1,2}.
Example 2: If U={1,2,3,4,5,6}, A={1,2,3}, then A′={4,5,6}. Always identify the universal set before finding a complement.
Important Results
For finite sets, n(A∪B)=n(A)+n(B)−n(A∩B). This avoids counting common elements twice.
Explained MCQs
- If A⊂B, which statement is necessarily true? Answer: Every element of A belongs to B. A subset condition concerns membership, not equality.
- If n(A)=12, n(B)=10 and n(A∩B)=4, then n(A∪B)=18. Calculation: 12+10−4=18.
- The complement A′ depends on: the universal set. Without U, the elements outside A cannot be determined uniquely.
Practice
- Let A={2,4,6,8} and B={4,8,12}. Find A∪B, A∩B and A−B.
- In a class of 40 students, 24 study Hindi, 18 study Sanskrit and 10 study both. Find how many study at least one.
Common Mistake
Do not confuse A−B with B−A; order matters.