Venn Diagrams and Sets

SETS ,VENN DIAGRAMS

by TEACHER JAMIE

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​WEEK 3 SEPT20

​UNIVERSAL SET

s a set that contains all the elements or objects of other sets, including its own elements. It is usually denoted by the symbol 'U'. Suppose Set A consists of all even numbers such that, A = {2, 4, 6, 8, 10, …} and set B consists of all odd numbers, such that, B = {1, 3, 5, 7, 9, …}.

​OVERLAPPING SET

​Two sets A and B are said to be overlapping if they contain at least one element in common.

EX. • A = {a, b, c, d}

B = {a, e, i, o, u}

​INTERSECTION OF SETS

​The intersection of a set A with a B is the set of elements that are in both set A and B. The intersection is denoted as A∩B.

​DISJOINT SETS

.Disjoint sets are sets that do not contain any common elements. Their intersection always results in an empty or null set. 

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​COMPLEMENT OF SETS

​The complement of set A is defined as a set that contains the elements present in the universal set but not in set A. For example, Set U = {2,4,6,8,10,12} and set A = {4,6,8}, then the complement of set A, A′ = {2,10,12}.

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1. Draw Venn diagrams to represent

(a) Union of sets (b) Intersection of sets Write steps of construction also.

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​(i) A (ii) B (iii) A (iv) B'

(v) A ∪ B (vi) A ∩ B (vii) (A ∪ B)'

(viii) (A ∩ B)' (ix) A - B

(x) B - A (xi) ξ

​(i) A (ii) B (iii) A (iv) B' (v) A ∪ B (vi) A ∩ B

(vii) (A ∪ B)' (viii) (A ∩ B)'

(ix) A - B(x) B - A (xi) ξ OR u

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4. In the adjoining Venn diagrams, find (a) A U B (b) A ∩ B