How to solve set problems without the aid of Venn diagrams?
In a school 70% of students like hamburgers, 60% like pizza. 50% of them like both, hamburger and pizza. How many percents like neither hamburger or pizza?
With the aid of a Venn diagram this problem is piece of cake but I'm having trouble creating a system of equations from these data. So can this problem be solved algebraically? How?
The set theory and algebra look like apple and oranges. Am I wrong?
Note: I'm studying mathematics at high-school level but any explanation would help, no matter how abstract/advanced it is.