Q.In a group of 100 people, 72 like coffee, 60 like tea, and 40 like both. Using a Venn diagram, find how many people like coffee only, tea only, and neither.

[!TLDR] Apply the union/difference formulas to a two-way survey. [!ANSWER] Coffee only $ …

Let $C$ = coffee drinkers, $T$ = tea drinkers, with $n(C)=72$, $n(T)=60$, $n(C \cap T) = 40$, total $=100$. Coffee only $= n(C) - n(C\cap T) = 72-40=32$. Tea only $= n(T) - n(C\cap T) = 60-40=20$. Total liking at least one: $n(C\cup T) = n(C)+n(T)-n(C\cap T) = 72+60-40=92$, so neither $= 100-92=8$. In a Venn diagram these four numbers — 32, 40, 20, 8 — fill the coffee-only region, the ove …

Break the total into the four disjoint Venn-diagram regions (coffee-only, overlap, tea-only, neit …

A common mistake is computing "coffee only" as simply $n(C)=72$, forgetting to remove the …