Module 6 · Modern Mathematics
Chapter 52: Set Theory
Modern Mathematics
3 topics
What this chapter covers
The 3 topics below make up Set Theory on the CAT. Click any topic to open its notes, examples and practice test.
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Formula Reference Sheet
This chapter
Counting & inclusion–exclusion
| Two-set union | n(A∪B) = n(A) + n(B) − n(A∩B) |
|---|---|
| Three-set union | n(A∪B∪C) = n(A)+n(B)+n(C) − n(A∩B) − n(B∩C) − n(C∩A) + n(A∩B∩C) |
| Neither / outside | n(neither) = Total − n(A∪B∪C) |
| Only A (two sets) | n(A only) = n(A) − n(A∩B) |
| Subsets of a set | A set with n elements has 2ⁿ subsets, 2ⁿ−1 proper |
Exactly-k & complement laws
| Exactly one (three sets) | Σn(A) − 2·Σn(A∩B) + 3·n(A∩B∩C) |
|---|---|
| Exactly two (three sets) | Σn(A∩B) − 3·n(A∩B∩C) |
| At least two | Σn(A∩B) − 2·n(A∩B∩C) |
| Complement | n(A') = n(U) − n(A) |
| De Morgan’s laws | (A∪B)' = A'∩B' ; (A∩B)' = A'∪B' |
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