Sets Relations And Functions Question 55
Question: Let R be a relation on the set N of natural numbers defined by nRm $ \Leftrightarrow $ n is a factor of m (i.e., n|m). Then R is
Options:
A) Reflexive and symmetric
B) Transitive and symmetric
C) Equivalence
D) Reflexive, transitive but not symmetric
Show Answer
Answer:
Correct Answer: D
Solution:
- Since n | n for all $ n\in N $ , therefore R is reflexive. Since 2 | 6 but $ 6\not{|}2 $ , therefore R is not symmetric. Let n R m and m R p Þ n|m and m|p Þ n|p Þ nRp. So, R is transitive.
BETA
