Priya is revising set notation for her exam. She writes two sets using set-builder notation: \(P = \{x : x \text{ is a prime number}, x < 20\}\) and \(Q = \...
Question 1 Report
Priya is revising set notation for her exam. She writes two sets using set-builder notation: \(P = \{x : x \text{ is a prime number}, x < 20\}\) and \(Q = \{x : x \text{ is a multiple of } 3, x < 20\}\).
- List the elements of \(P\). (1)
- List the elements of \(Q\). (1)
- Write down \(P \cap Q\). (1)
Answer Details
Set-builder notation describes each set by a defining property. Listing the elements of \(P\) and \(Q\) directly makes their intersection straightforward to identify.
- The prime numbers less than 20 (numbers with exactly two factors, 1 and themselves):\[ P = \{2, 3, 5, 7, 11, 13, 17, 19\} \][1]
- The multiples of 3 less than 20:\[ Q = \{3, 6, 9, 12, 15, 18\} \][1]
- The only value appearing in both lists is 3, which is both prime and a multiple of 3:\[ P \cap Q = \{3\} \][1]
The number 1 is not prime (it has only one factor, itself), so it must be excluded from \(P\); forgetting this rule and including 1 is a common way marks are lost when a question involves listing primes.
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