Set EduRev's Tips
The number of elements in a set is called its cardinal number and is written as n(A). A set with cardinal number 0 is called a null set while that with cardinal number ∞ is called an infinite set.
Set A is said to be a subset of Set B if each and every element of Set A is also contained in Set B. Set A is said to be a proper subset of Set B if Set B has at least one element that is not contained in Set A. A set with ‘n’ elements will have 2^{n} subsets (2^{n} – 1 proper subsets)
The Universal set is defined as the set of all possible objects under consideration.
EduRev's Tip: Any set is a subset of itself, but not a proper subset. The empty set, denoted by ∅ , is also a subset of any given set X. The empty set is always a proper subset, except of itself. Every other set is then a subset of the universal set.
Union of two sets is represented as A ∪ B and consists of elements that are present in either Set A or Set B or both. Intersection of two sets is represented as A ∩ B and consists of elements that are present in both Set A and Set B. n(A ∪ B) = n(A) + n(B) — n(A ∩ B)
Venn Diagram: A venn diagram is used to visually represent the relationship between various sets. What do each of the areas in the figure represent?
I – only A; II – A and B but not C; III – Only B; IV – A and C but not B; V – A and B and C; VI – B and C but not A; VII – Only C
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) — n(A ∩ B) — n(A ∩ C) n(B ∩ C) + n(A ∩ B ∩ C)
For some basic values:
Theorem
(a + b)^{n} =
Some basic properties
EduRev's Tip:
207 videos156 docs192 tests

1. What are the basic operations in set theory? 
2. What is the cardinality of a set? 
3. What is the power set of a set? 
4. What is the difference between a subset and a proper subset? 
5. What is the Universal Set in set theory? 
207 videos156 docs192 tests


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