Venn diagrams for Sets

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.

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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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