Question

If A has 4 elements B has 8 elements then the minimum and maximum number of elements in A U B

Answer 1

$Given \: number \:of \: elements \: in \: Set \:A = 4$

$number \:of \: elements \: in \: Set \:B = 8$

$\blue{i) Minimum \: number \: of \: elements \: in}$

$\blue{ set \: A\cup B = 8}$

$\green{ ii) Maximum \: number \: of \: elements \: in}$

$\green {set \: A\cup B = 12}$

Examples:

1. Let set A = { 1,2,3,4} , B = { 1,2,3,4,5,6,7,8}.

AUB = { 1,2,3,4} U {1,2,3,4,5,6,7,8 }

= { 1,2,3,4,5,6,7,8 }

Now, number of elements in AUB = 8 (minimum)

2. Let set A = { 1,2,3,4} , B = { 5,6,7,8,9,10,11,12}.

AUB = { 1,2,3,4} U {5,6,7,8,9,10,11,12}

= { 1,2,3,4,5,6,7,8,9,10,11,12 }

Now, number of elements in AUB = 12 (Maximum)

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Answer 2

Answer:

wGiven \: number \:of \: elements \: in \: Set \:A = 4GivennumberofelementsinSetA=4

number \:of \: elements \: in \: Set \:B = 8numberofelementsinSetB=8

\blue{i) Minimum \: number \: of \: elements \: in}i)Minimumnumberofelementsin

\blue{ set \: A\cup B = 8}setA∪B=8

\green{ ii) Maximum \: number \: of \: elements \: in}ii)Maximumnumberofelementsin

\green {set \: A\cup B = 12}setA∪B=12

Examples:

1. Let set A = { 1,2,3,4} , B = { 1,2,3,4,5,6,7,8}.

AUB = { 1,2,3,4} U {1,2,3,4,5,6,7,8 }

= { 1,2,3,4,5,6,7,8 }

Now, number of elements in AUB = 8 (minimum)

2. Let set A = { 1,2,3,4} , B = { 5,6,7,8,9,10,11,12}.

AUB = { 1,2,3,4} U {5,6,7,8,9,10,11,12}

= { 1,2,3,4,5,6,7,8,9,10,11,12 }

= { 1,2,3,4,5,6,7,8,9,10,11,12 }

Now, number of elements in AUB = 12 (Maximum)

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