1.7 Cardinality and Practical Problems

Let $n(H)=25, n(T)=26, n(I)=26$. Intersections: $n(H \cap I)=9, n(H \cap T)=11, n(T \cap I)=8$. All three: $n(H \cap T \cap I)=3$.

Using Venn Diagram Formula for "Only A": $n(\text{Only H}) = n(H) - n(H \cap T) - n(H \cap I) + n(H \cap T \cap I)$ $= 25 - 11 - 9 + 3 = 8$

$n(\text{Only T}) = n(T) - n(T \cap H) - n(T \cap I) + n(T \cap H \cap I)$ $= 26 - 11 - 8 + 3 = 10$

$n(\text{Only I}) = n(I) - n(I \cap H) - n(I \cap T) + n(I \cap H \cap T)$ $= 26 - 9 - 8 + 3 = 12$

Total reading exactly one = $8 + 10 + 12 = 30$.