Venn diagrams for sets is useful in understanding various relations between sets. A universal set is expressed by the interior part of a rectangle. Other sets ( like subsets of the universal set) are expressed by circular regions contained in the rectangle.

Venn diagrams for sets

1)**Subset **

**Example : **

Set A = { 2,4 } is a subset of universal set &xi = { 1, 2, 3, 4 }.

• First draw a rectangle. It is a universal set denoted as ξ .

• As set A is a subset of ξ, so draw a circle inside it.

• Write all the element of set A inside the circle.

• Write the elements of ξ which are other than set A in the rectangle.

2)**Disjoint sets **

**Example : **

ξ = { 1, 2, 3, 4, 5, 6, 7} , Set A = { 2, 4, 6, } and set B = {1, 3, 5} .

• First draw a rectangle. It is a universal set denoted as ξ .

• As there are two sets so, draw two circles inside the rectangle, A and B.

• Inside A write its elements and inside B write its elements.

• Write the elements of ξ which are other than set A and set B in the rectangle.

3)**Overlapping sets **

**Example : **

ξ = { a, b, c, d, e } , A ={ a, b } and B = { b, c ,d } • First draw a rectangle. It is a universal set denoted as ξ .

• As there are two sets so, draw two circles inside the rectangle, A and B.

• Inside A write its elements and inside B write its elements.

• As the two sets contain some common elements so the two circles intersect each other. The common element write in that intersection region.

• Write the elements of ξ which are other than set A and set B in the rectangle.

**Set Theory **

• Sets

• Representation of Set

• Cardinal Number

• Types of Sets

• Pairs of Sets

• Subset

• Complement of Set

• Union of the Sets

• Intersection of Sets

• Operations on Sets

• De Morgan's Law

• Venn Diagrams

• Venn diagrams for sets

• Venn-diagrams for different situations

• Problems on Intersection of Two Sets

• Problems on Intersection of Three Sets

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Venn diagrams for sets

1)

Set A = { 2,4 } is a subset of universal set &xi = { 1, 2, 3, 4 }.

• First draw a rectangle. It is a universal set denoted as ξ .

• As set A is a subset of ξ, so draw a circle inside it.

• Write all the element of set A inside the circle.

• Write the elements of ξ which are other than set A in the rectangle.

2)

ξ = { 1, 2, 3, 4, 5, 6, 7} , Set A = { 2, 4, 6, } and set B = {1, 3, 5} .

• First draw a rectangle. It is a universal set denoted as ξ .

• As there are two sets so, draw two circles inside the rectangle, A and B.

• Inside A write its elements and inside B write its elements.

• Write the elements of ξ which are other than set A and set B in the rectangle.

3)

ξ = { a, b, c, d, e } , A ={ a, b } and B = { b, c ,d } • First draw a rectangle. It is a universal set denoted as ξ .

• As there are two sets so, draw two circles inside the rectangle, A and B.

• Inside A write its elements and inside B write its elements.

• As the two sets contain some common elements so the two circles intersect each other. The common element write in that intersection region.

• Write the elements of ξ which are other than set A and set B in the rectangle.

• Sets

• Representation of Set

• Cardinal Number

• Types of Sets

• Pairs of Sets

• Subset

• Complement of Set

• Union of the Sets

• Intersection of Sets

• Operations on Sets

• De Morgan's Law

• Venn Diagrams

• Venn diagrams for sets

• Venn-diagrams for different situations

• Problems on Intersection of Two Sets

• Problems on Intersection of Three Sets