Find the smallest set A such that A - 1-2-1-2-3-5-9

The smallest set A such that A ∪ 1,2 = 1,2,3,5,9 is 3.5.9 ∴ 3,5,9 ∪ 1,2 = 1,2,3,5,9 Any other set B such that B ∪ 1,2 = 1,2,3,5,9 will contain A. For example we ...

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Standard XII

Mathematics

Union

Find the smal...

Question

Find the smallest set A such that $A \cup$

{1,2} = {1,2,3,5,9}

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Solution

The smallest set A such that

$A \cup$ {1,2} = {1,2,3,5,9} is {3.5.9}

$∴$ {3,5,9} $\cup$ {1,2} = {1,2,3,5,9}

Any other set B such that $B \cup$ {1,2} = {1,2,3,5,9} will contain A. For example we can take B to be {1,3,5,9} or {1,2,3,5,9} Clearly B contains A = {3,5,9}.

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Find the smallest set A such that A ∪ {1,2} = {1,2,3,5,9}

The smallest set A such that A ∪ {1,2} = {1,2,3,5,9} is {3.5.9} ∴ {3,5,9} ∪ {1,2} = {1,2,3,5,9} Any other set B such that B ∪ {1,2} = {1,2,3,5,9} will contain A. For example we can take B to be {1,3,5,9} or {1,2,3,5,9} Clearly B contains A = {3,5,9}.

Find the smallest set A such that $A \cup$

{1,2} = {1,2,3,5,9}

The smallest set A such that

$A \cup$ {1,2} = {1,2,3,5,9} is {3.5.9}

$∴$ {3,5,9} $\cup$ {1,2} = {1,2,3,5,9}

Any other set B such that $B \cup$ {1,2} = {1,2,3,5,9} will contain A. For example we can take B to be {1,3,5,9} or {1,2,3,5,9} Clearly B contains A = {3,5,9}.