1. ## relations help (4)

hey guys, question:

Determine whether the following relation is a reflexive, symmetric or transitive. If any is an equivalence relation, describe its equivalence classes.

xRy iff x is a multiple of y, on

Is it reflexive? Yes, since x is a multiple of x
Is it symmetric? No, since if x is a multiple of y, then y is not a multiple of x.

2. Originally Posted by jvignacio
hey guys, question:

Determine whether the following relation is a reflexive, symmetric or transitive. If any is an equivalence relation, describe its equivalence classes.

xRy iff x is a multiple of y, on

Is it symmetric? No, since if x is a multiple of y, then y $\displaystyle \color{red} need not be}$ a not a multiple of x.
Sure, it is transitive because xRy and yRz means that there exist $\displaystyle n, m\in \mathbb{Z}$, such that $\displaystyle x=ny$ and $\displaystyle y=mz$. It follows that $\displaystyle x=m\cdot n\cdot z=(mn)\cdot z$, thus x is a multiple of z, i.e. xRz.