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Answered

Let the universal Set be s. Let A and B are subsets of S. Set contains 90 elements and Set B contains 99 elements. Set A and B have 21 elements in common. If there are 24 elements that are in S but not in A nor B, how many elements are in S ?

Answer :

Given

Set A contains = 90 elements

Set B contains = 99 elements

A and B contains = 21 elements

Find

number of elements in Set S

Explanation

As we know

[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]

so,

[tex]n(A\cup B)=90+99-21=168[/tex]

Total elements in S = elements in A or B + elements not in A or B

so,

[tex]168+24=192[/tex]

Final Answer

Total elements in S = 192

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