If $P$ is the multiples of 5 below 35 and $Q$ the odd numbers between 14 and 30, then $P\cap Q$ is:
A$\{5,15,25\}$
B$\{15,17,25\}$
C$\{15,25\}$
D$\{5,10,15,25\}$
Answer & Solution
Correct answer: C. $\{15,25\}$
1. List $P$, the multiples of 5 below 35: $\{5,10,15,20,25,30\}$.
2. List $Q$, the odd numbers strictly between 14 and 30: $\{15,17,19,21,23,25\}$.
3. The intersection holds only members appearing in both lists.
4. Checking each element of $P$: 15 and 25 are odd and lie in range; 5 and 10 are below 14, and 20 and 30 are even.
5. So $P\cap Q=\{15,25\}$.
_Source: NECTA CSEE 2022 Basic Mathematics 041, Question 3: Sets and Probability_
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