Set Theory
🇬🇧
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Set Theory - Leaderboard
Set Theory - Details
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| 🇬🇧 | 🇬🇧 |
| The number of distinct element in aset which is denoted by n(V) or |V|. | Cardinality of a Set |
| A set which contains only one element is known as | Singleton sets |
| The sets in which number of elements are limited and can be counted, such sets are called | Finite sets |
| The sets in which number of elements are unlimited and can not be counted, such sets are called | Infinite sets |
| If two sets have no element in common. | Disjoint Sets |
| A set that contains all sets under consideration as a subset denoted by ξ or U is called | Universal Set |
| Cartesian Product of Sets | A x B = {(a,b) / a ɛ A and b ɛ B} |
| The set consisting of all elements which are in both sets A and B. It is denoted by A ∩ B | Intersection of Sets |
| The set of all elements in the universal set that are not in A. It is denoted by A’ | Complement of a Set w.r.t. Universal Set |
| The set of all elements in the set B but not in A. It is denoted by B\A | Complement of a Set A w.r.t. another set B |
| |A U B| = |A|+ |B|- |A ∩B| | Inclusion- Exclusion Principle for twoSets |
| |A U B U C| = |A|+ |B|+|C|- |A ∩B|-|A ∩C| - |B ∩C|+ |A ∩ B ∩ C| | Inclusion- Exclusion Principle for three Sets |