To draw Venn diagrams in different situations are discussed below:

How to represent a set using Venn diagrams in different situations?

**1. ξ is a universal set and A is a subset of the universal set.**

ξ = {1, 2, 3, 4}

A = {2, 3} **•** Draw a rectangle which represents the universal set. **•** Draw a circle inside the rectangle which represents A. **•** Write the elements of A inside the circle. **•** Write the leftover elements in ξ that is outside the circle but inside the rectangle. **•** Shaded portion represents A’, i.e., A’ = {1, 4}

**2. ξ is a universal set. A and B are two disjoint sets but the subset of the universal set i.e., A ⊆ ξ, B ⊆ ξ and A ∩ B = ф**

**For example;**

ξ = {a, e, i, o, u}

A = {a, i}

B = {e, u} **•** Draw a rectangle which represents the universal set. **•** Draw two circles inside the rectangle which represents A and B. **•** The circles do not overlap. **•** Write the elements of A inside the circle A and the elements of B inside the circle B of ξ. **•** Write the leftover elements in ξ , i.e., outside both circles but inside the rectangle. **•** The figure represents A ∩ B = ф

**3. ξ is a universal set. A and B are subsets of ξ. They are also overlapping sets.**

**For example;**

Let ξ = {1, 2, 3, 4, 5, 6, 7}

A = {2, 4, 6, 5} and B = {1, 2, 3, 5}

Then A ∩ B = {2, 5} **•** Draw a rectangle which represents a universal set. **•** Draw two circles inside the rectangle which represents A and B. **•** The circles overlap. **•** Write the elements of A and B in the respective circles such that common elements are written in overlapping portion (2, 5). **•** Write rest of the elements in the rectangle but outside the two circles. **•** The figure represents A ∩ B = {2, 5}

**4. ξ is a universal set and A and B are two sets such that A is a subset of B and B is a subset of ξ.**

**For example;**

Let ξ = {1, 3, 5, 7, 9}

A= {3, 5} and B= {1, 3, 5}

Then A ⊆ B and B ⊆ ξ **•** Draw a rectangle which represents the universal set. **•** Draw two circles such that circle A is inside circle B as A ⊆ B. **•** Write the elements of A in the innermost circle. **•** Write the remaining elements of B outside the circle A but inside the circle B.

**•** The leftover elements of are written inside the rectangle but outside the two circles. **Observe the Venn diagrams. The shaded portion represents the following sets. **

(a) **A’** (A dash)

(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 dash)

(g) **A - B** (A minus B)

(h) **(A - B)’ ** (Dash of sets A minus B)

(i) **(A ⊂ B)’ **(Dash of A subset B)

**For example;**

**Use Venn diagrams in different situations to find the following sets. **

(a) A ∪ B

(b) A ∩ B

(c) A'

(d) B - 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}**B - A** = {elements which are in B but not in A}

= {e, g} **(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}

● **Set Theory**

**● ****Finite Sets and Infinite Sets**

**● ****Problems on Intersection of Sets**

**● ****Problems on Complement of a Set**

**● ****Problems on Operation on Sets**

**● ****Venn Diagrams in Different
Situations**

**● ****Relationship in Sets using Venn
Diagram**

**● ****Union of Sets using Venn Diagram**

**● ****Intersection of Sets using Venn
Diagram**

**● ****Disjoint of Sets using Venn
Diagram**

**● ****Difference of Sets using Venn
Diagram**

**8th Grade Math Practice**

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