MATH SOLVE

4 months ago

Q:
# Let the Universal Set, S, have 203 elements. A and B are subsets of S. Set A contains 98 elements and Set B contains 81 elements. If the total number of elements in either A or B is 173, how many elements are in A but not in B?

Accepted Solution

A:

Answer: There are 92 elements in A but not in B.Step-by-step explanation:Since we have given that n(S) = 203n(A) = 98n(B) = 81n(A∪ B) = 173We first find the value of n(A∩B).[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)\\\\173=98+81-n(A\cap B)\\\\173=179-n(A\cap B)\\\\173-179=-n(A\cap B)\\\\6=n(A\cap B)[/tex]We need to find the number of elements that are in A but not in B.[tex]n(A-B)=n(A)-n(A\cap B)\\\\n(A-B)=98-6\\\\n(A-B)=92[/tex]Hence, there are 92 elements in A but not in B.