(Solved): The accompanying Venn diagram shows the number of elements in region V. Use the given cardinalitie ...

The accompanying Venn diagram shows the number of elements in region V. Use the given cardinalities to determine the number of elements in each of the other seven regions. \[ \begin{array}{l} n(\mathrm{U})=44, n(\mathrm{~A})=28, n(\mathrm{~B})=18 \\ n(\mathrm{C})=21, n(\mathrm{~A} \cap \mathrm{B})=11 \\ n(\mathrm{~A} \cap \mathrm{C})=15, n(\mathrm{~B} \cap \mathrm{C})=10 \end{array} \] There are elements in region I. There are elements in region II. There are elements in region III. There are elements in region IV. There are elements in region \( \mathrm{VI} \). There are elements in region VII. There are elements in region VIII.