The relation R on real numbers given by
xRy <=> x-y E(belongs) to Q
can you help me with Symmetric and Transitive?
Someone told me this is how to show its symmectric
x-y = a/b
-(x-y) = y-x = -a/b
cant figure out transitive?
The relation R on real numbers given by
xRy <=> x-y E(belongs) to Q
can you help me with Symmetric and Transitive?
Someone told me this is how to show its symmectric
x-y = a/b
-(x-y) = y-x = -a/b
cant figure out transitive?
Here is something that you could do almost without thinking.
The definition of a transitive relation applied to R: for any three numbers x, y, z, if $\displaystyle x-y\in\mathbb{Q}$ and $\displaystyle y-z\in\mathbb{Q}$, then $\displaystyle x-z\in\mathbb{Q}$. One has to prove this. Let's fix some numbers x, y and z and assume that $\displaystyle x-y\in\mathbb{Q}$ and $\displaystyle y-z\in\mathbb{Q}$. This means there are rational numbers a / b and c / d such that x - y = a / b and y - z = c / d. One has to prove that x - z is a rational number.
Here you actually turn on the brain: x - z = (x - y) + (y - z). Is this number rational?