Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 115, n(B) = 90, and n(A ∩ B) = 50. Find the number of

Question

sergejj [24]

3 years ago

9

Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 115, n(B) = 90, and n(A ∩ B) = 50. Find the number of

elements in the set.

Mathematics

1 answer:

babunello [35] · Answer 1 · 2022-01-29T01:22:13+03:00

By the inclusion/exclusion principle,

$n(A\cup B)=n(A)+n(B)-n(A\cap B)=155$

There are 400 elements in the universal set $U$ , which means there are 400 - 155 = 245 elements not accounted for by $A\cup B$ , or

$n(U)=n(A\cup B)+n((A\cup B)^C)\implies n((A\cup B)^C)=245$

That's all you can really determine from the given info. Considering the language of the problem, "Find the number of elements in the set", I find it hard to believe that the set it's talking about isn't mentioned.