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 2n subsets (2n – 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:
(a + b)n =
Some basic properties