Let $R$ be the binary relation on $\mathbb{N}$ defined by $xRy$ ($x$ is in relation to $y$) defined by: $xRy$ if $xy=49$

Question

A) $R$ is reflexive and $R$ is symmetric

B) $R$ is reflexive and $R$ is not symmetric

C) $R$ is not reflexive and $R$ is symmetric

D) $R$ is not reflexive and $R$ is not symmetric

The answer is C. I understand why it is symmetric, but why it is not reflexive? For example, if I have $xy=7\times7=49$ (which is reflexive relation, isn't it?). Anyone explain please?

Thank You

What is the definition of a reflexive relation? – pjs36 Feb 26 '17 at 01:44 — pjs36, Feb 26 '17 at 01:44

score 3 · Accepted Answer · answered Feb 26 '17 at 02:01

3

For a relation $R$ to be reflexive means that $xRx$ for ALL $x$ in the domain of the relation. Yes, it's true that in this example $x=7$ satisfies $xRx$ because $7\cdot7=49$. But is it true that $xRx$ for ALL $x\in\mathbb{N}$? I.e., is it true that for all natural numbers $x^2=49$?

answered Feb 26 '17 at 02:01

zipirovich

14,670
1
26
35

1

I got it. Thank You so much! – pkim Feb 26 '17 at 02:03

score 2 · Answer 2 · answered Feb 26 '17 at 02:00

2

Reflexive is: $\forall x$, $xRx$.

Find an $x$ such that $x^2 \ne 49$

answered Feb 26 '17 at 02:00

Rustyn

8,407

Let $R$ be the binary relation on $\mathbb{N}$ defined by $xRy$ ($x$ is in relation to $y$) defined by: $xRy$ if $xy=49$

2 Answers2