MediumMathematicsHigh School (11–12)Functions and Calculus › Sets and IntervalsNumericalBoard Exam SAT

In a group of 80 students, 46 like football, 38 like cricket and 20 like both.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

In a group of $80$ students, $46$ like football, $38$ like cricket and $20$ like both. How many like neither? How many like only football?

Need a reminder? The key ideaShow

$n(A \cup B) = n(A) + n(B) - n(A \cap B)$ . A set of $n$ elements has $2^n$ subsets. De Morgan: $(A \cup B)' = A' \cap B'$ and $(A \cap B)' = A' \cup B'$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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