‹ Back to the paper
Choose the correct option.
A relation R is defined on mathbbZ as a R b if and only if a² - 7ab + 6b² = 0. Then R is:
A relation $R$ is defined on $\mathbb{Z}$ as $a R b$ if and only if $a^2 - 7ab + 6b^2 = 0$.
Then $R$ is:
- areflexive and symmetric
- btransitive but not reflexive
- csymmetric but not reflexive
- dreflexive but not symmetric
Answer
Answer
Official answer keyCorrect option: d
Answer: (d) reflexive but not symmetric
Reflexive: $a^2 - 7a\cdot a + 6a^2 = 0$ for every $a \in \mathbb{Z}$, so $(a,a) \in R$.
Not symmetric: $(6,1)$ gives $36 - 42 + 6 = 0$, so $(6,1) \in R$, but $(1,6)$ gives $1 - 42 + 216 \neq 0$, so $(1,6) \notin R$.