2026 SPS P1 Q24

\(\xi=\{x:x\text{ is an integer},1\leq x\leq12\}\)

\(A=\{x:x\text{ is a multiple of}\hspace{0.5em}3\}\)

\(B=\{x:x\text{ is a factor of}\hspace{0.5em}12\}\)

\(C=\{x:x\text{ is a prime number greater than}\hspace{0.5em}6\}\)

1. Find \(n((A\cup B)\prime)\).[1]
2. List the elements of \(A\prime\cap B\).[1]
3. State whether the statement “\(9\in A\cap B\prime\)” is true or false, justifying your answer.[1]
4. An integer is chosen at random from \(\xi\).
   Event X: the chosen integer belongs to set B. Event Y: the chosen integer belongs to set C.
   Determine whether events X and Y are mutually exclusive. Give a reason for your answer.[1]