venn diagrams for sets

Venn diagrams for Sets

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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