Introduction to Sets

Types of sets

• Empty set or null set: It has no element present in it.
• Finite set: It has a limited number of elements.
• Infinite set: It has an infinite number of elements.
• Equal set: Two sets that have the same members.
• Subsets: A set ‘\(A\)’ is called to be a subset of \(B\) if each element of \(A\) is also an element of \(B\).
• Universal set: A set that consists of all elements of other sets present in a Venn diagram.

Sets formulas

• \(\color{blue}{n\left(A\:U\:B\right)=\:n\left(A\right)\:+\:n\left(B\right)-\:n\left(A\:∩\:B\right)}\)
• \(\color{blue}{n\:\left(A\:∩\:B\right)=n\left(A\right)+n\left(B\right)-n\left(A\:U\:B\right)}\)
• \(\color{blue}{n\left(A\right)=n\left(A\:U\:B\right)+n\left(A\:∩\:B\right)-\:n\left(B\right)}\)
• \(\color{blue}{n\left(B\right)=\:n\left(A\:U\:B\right)+n\left(A\:∩\:B\right)-\:n\left(A\right)}\)
• \(\color{blue}{n\left(A\:-\:B\right)=n\left(A\:U\:B\right)-n\left(B\right)}\)
• \(\color{blue}{n\left(A\:-\:B\right)=\:n\left(A\right)-\:n\left(A\:∩\:B\right)}\)

For any two sets \(A\) and \(B\) that are disjoint,

• \(\color{blue}{n\left(A\:U\:B\right)=n\left(A\right)+\:n\left(B\right)}\)
• \(\color{blue}{A ∩ B = ∅}\)
• \(\color{blue}{n\left(A\:-\:B\right)=n\left(A\right)}\)

Sets – Example 1:

 If set \(A=\) {\(a,b,c\)} and set \(B=\) {\(a,b,c,l,z,r\)}, find \(A ∩ B\).

Solution:

\(A∩B=\) {\(a,b,c\)}