A universal set $\xi$ contains $40$ elements. $$n(A\cap B')=12,$$$$n(A'\cap B)=9,$$\[n((A\c

Question

A universal set $\xi$ contains $40$ elements. $$n(A\cap B')=12,$$$$n(A'\cap B)=9,$$$$n((A\cap B)')=33.$$ Find $n(A\cap B)$. Find $n((A\cup B)')$. Complete the four region counts of a Venn diagram. Find $n(A'\cup B)$. A student claims that the answer to part (d) is $$ n(A')+n(B). $$ Explain the error and identify how many elements this method counts twice.

Accepted Answer

(a) $7$ (b) $12$ (c) $(12,7,9,12)$* (d) $28$ (e) B-only elements are counted twice: $9$

Sets

Sets