Probability, 2ADV EQ-Bank 3

Consider the universal set \(U=\{x\) is a positive integer and \(x \leqslant 15\}\)

Three sets are defined as:

\begin{aligned}
& A=\{x \text { is a multiple of } 3\} \\
& B=\{x \text{ is a prime number}\} \\
& C=\{x \text{ is even}\}
\end{aligned}

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

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Find \(B \cap C\) (1 mark)

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Find \(A \cup \overline{C}\) (2 marks)

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Show Answers Only

a. \(A=\{3,6,9,12,15\}\)

b. \(B \cap C = \{2\} \)

c. \(A \cup \overline{C}=\{1,3,5,6,7,9,11,12,13,15\}\)

Show Worked Solution

a. \(A=\{3,6,9,12,15\}\)

b. \(B=\{2,3,5,7,11,13\}\)

\(C=\{2,4,6,8,10,12,14\}\)

\(B \cap C = \{2\} \)

c. \(\text{Find} \ \ A \cup \overline{C}:\)

\(\overline{C}=\{1,3,5,7,9,11,13\}\)

\(A \cup \overline{C}=\{1,3,5,6,7,9,11,12,13,15\}\)