Question on: SS1 Mathematics - Elementary Set Theory
In a school Interhouse competition, 80% of the students turned up at the athletic competition, 60% turned up at the football match. What percentage of the students attended both functions?
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The universal set \(U\) is \(100\%\) of students at the Interhouse sports competition
\[n(U) = 100\%\]
\(n(A) = 80\%\), percentage of students at the athletic competition.
\(n(F) = 60\%\), percentage of students at the football competition.
\(n(A \cap F) = x\), percentage that attended both.
\[n(U) = \ n(A) + n(F) - n(A \cap F)\]
\[100\% = 80\% + 60\% - x\]
\[100\% = 140\% - x\]
\[100\% - 140\% = - x\]
\[- 40\% = - x\]
\(x = 40\%\)
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