Sets Relations And Functions Question 108
Question: Let S be a set of all distinct numbers of the form $\frac{P}{Q}$, where $p, q \in \{1,2,3,4,5,6\}$. What is the cardinality of the set S ?
Options:
A) 21
B) 23
C) 32
D) 36
Show Answer
Answer:
Correct Answer: B
Solution:
- [b]
There are 6 x 6 = 36 possible fractions initially.
We need to exclude fractions that reduce to the same value (like 2/4 = 1/2).
We also include whole numbers (when P is divisible by Q).
After accounting for all unique fractions and whole numbers, we get 23 distinct values in set S.
BETA
