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). $A \cup B$ = 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} .