Q.In a survey of 50 students, 30 like tea, 25 like coffee, and 10 like both tea and coffee. Using set operations, find

[!TLDR] Use $n(T\cup C)=n(T)+n(C)-n(T\cap C)$ for a survey word problem. [!ANSWER] 5 students …

Let $T$ = students who like tea, $C$ = students who like coffee, with $n(T)=30$, $n(C)=25$, $n(T \cap C)=10$, and total students $=50$. By the union formula, $n(T \cup C) = n(T)+n(C)-n(T \cap C) = 30+25-10 = 45$, so 45 students like at least one drink, leaving $50-45=5$ students who like neither. The number w …

Translate the word problem into set sizes, apply the union formula to find "at least one," then subtract from the total for "neither," an …

A very common mistake is adding $30+25=55$ directly as "at least one," forgetting to subtract the …