Set
CBSE · Class 11 · Applied Mathematics
Quick revision notes for Set — CBSE Class 11 Applied Mathematics. Key concepts, formulas, and definitions for last-minute revision.
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Key Topics to Revise
Definition and Representation of Sets
- A set is a well-defined collection of distinct objects called elements or members
- Well-defined means we can clearly identify whether an object belongs to the set or not
- Elements are distinct - no repetition is allowed in a set
Types of Sets
- Empty Set (∅ or {}): Contains no elements, n(∅) = 0
- Singleton Set: Contains exactly one element
- Finite Set: Has definite number of elements that can be counted
Subsets and Set Relations
- A ⊆ B means every element of A is also in B
- A ⊂ B means A is a proper subset of B (A ⊆ B but A ≠ B)
- Every set is a subset of itself: A ⊆ A
Intervals as Subsets of Real Numbers
- Closed interval [a,b]: includes both endpoints a and b
- Open interval (a,b): excludes both endpoints a and b
- Semi-open intervals: [a,b) includes a, excludes b; (a,b] excludes a, includes b
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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