Sets: Notes

• The intersection of two sets can be represented by Venn diagram, with the shaded region representing A ∩ B.

A ∩ B when A ⊂ B, i.e., A ∩ B = A

A ∩ B when neither A ⊂ B nor B ⊂ A

A ∩ B = ϕ No shaded part



• The union of two sets can be represented by Venn diagrams by the shaded region, representing A ∪ B.

A ∪ B when A ⊂ B

A ∪ B when neither A ⊂ B nor B ⊂ A

A ∪ B when A and B are disjoint sets



Relationship between the three Sets using Venn Diagram
• If ξ represents the universal set and A, B, C are the three subsets of the universal sets. Here, all the three sets are overlapping sets.

Let us learn to represent various operations on these sets.

A ∪ B ∪ C

A ∩ B ∩ C

A ∪ (B ∩ C)

A ∩ (B ∪ C)










Observe the Venn diagrams. The shaded portion represents the following sets.

(a) A’ (A prime)

(b) A ∪ B (A union B)

(c) A ∩ B (A intersection B)

(d) (A ∪ B)’ (A union B dash)

(e) (A ∩ B)’ (A intersection B dash)

(f) B’ (B prime)

For example;
Use Venn diagrams in different situations to find the following sets.

(a) A ∪ B

(b) A ∩ B

(c) A'

(e) (A ∩ B)'

(f) (A ∪ B)'

Solution:

ξ = {a, b, c, d, e, f, g, h, i, j}

A = {a, b, c, d, f}

B = {d, f, e, g}

A ∪ B = {elements which are in A or in B or in both}

         = {a, b, c, d, e, f, g}

A ∩ B = {elements which are common to both A and B}

        = {d, f}

A' = {elements of ξ, which are not in A}

    = {e, g, h, i, j}


(A ∩ B)' = {elements of ξ which are not in A ∩ B}

            = {a, b, c, e, g, h, i, j}

(A ∪ B)' = {elements of ξ which are not in A ∪ B}

             = {h, i, j}