Let S be the following ordered sequence of elements S = {1, 2, 3, 4, 5, 6} and the universal set U be {1, 2, 3, 4, 5, 6}. Write down the characteristic vectors of • A = {1, 2, 4, 5}; • B = {3, 5}; • ∅; • A ∪ B; • A ∩ B; • A∪ ∼ B; • A∆B.
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A). ∅ denotes empty set or null set. The empty set contains no element
B). = it means that it contains the element having in both sets
A union B or A U B = { 1,2,3,4,5}.
C) A ∩ B = A intersection B
= contains element that are common to both sets
= {5} .
D) given that A ={1,2,4,5} , B= {3,5}
~ B = { 1,2,4,6}
now, A union ( ~B) = A U ~B
= element that are common to both sets A and ~B.
= { 1,2,4}.
E) let A and B be two sets. The symmetric difference of two sets A and B is the ( A-B) U ( B-A).
A-B = remove elements from set A Which are present in set B ( i.e, 5)
A-B = { 1,2,4}
:: B-A = remove elements from set B Which are present in set A ( i.e, 5)
B-A= { 3,5} -{1,2,4,5} = {3}
( A-B) U ( B-A) = {1,2,4} U {3}
= { 1,2,3,4} .