Probability, 2ADV EQ-Bank 13

Consider the universal set \(U=\{x\) is a positive integer and \(x \leqslant 24\}\)

Three sets are defined as

\begin{aligned}
& A=\{x \text { is a factor of } 24\} \\
& B=\{x \text { is a perfect square}\} \\
& C=\{x \text { is divisible by } 3\}
\end{aligned}

List the elements of set \(A\). (1 mark)

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Find \(A \cap B\). (1 mark)

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Find \((A \cup B) \cap C^c\) (2 marks)

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Show Answers Only

a. \(A=\{1,2,3,4,6,8,12,24\}\)

b. \(A \cap B=\{1,4\}\)

c. \((A \cup B) \cap C^c=\{1,2,4,8,16\}\)

Show Worked Solution

a. \(A=\{1,2,3,4,6,8,12,24\}\)

b. \(B=\{1,4,9,16\}\)

\(A \cap B=\{1,4\}\)

c. \(A \cup B=\{1,2,3,4,6,8,9,12,16,24\}\)

\(C=\{3,6,9,12,15,18,21,24\}\)

\(C^c=\{1,2,4,5,7,8,10,11,13,14,16,17,19,20,22,23\}\)

\((A \cup B) \cap C^c=\{1,2,4,8,16\}\)