Elementary Set Theory - SS1 Mathematics Past Questions and Answers - page 1

Given \(U = \left\{ 4,6,8,10,12,15,19 \right\},\ \)

\[C = \left\{ 4,6,8 \right\},\]

\[D = \left\{ 10,12,6,15 \right\}\ \]

\[E = \{ 4,15,19,6,10\}\]

(a) \(C \cap D = \{ 6\}\)

(b) \(D \cup E = \{ 4,6,10,12,15,19\}\)

(c) \(\ C - D = \{ 4,8\}\)

(d) \(D^{'} = \{ 4,8,19\}\)

(e) \(P(C) = \ 2^{3} = 8 = \ \varnothing,\ \left\{ 4 \right\},\ \left\{ 6 \right\},\ \left\{ 8 \right\},\ \left\{ 4,6 \right\},\ \left\{ 4,8 \right\},\ \left\{ 6,8 \right\},\ \{ 4,6,8\}\)

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.

\[n(U) = \ n(A) + n(F) - n(A \cap F)\]

\[100\% = 80\% + 60\% - x\]

\[100\% = 140\% - x\]

\[100\% - 140\% = - x\]

\[- 40\% = - x\]

\(x = 40\%\)