 # I'm having trouble with this math problem on equivalence relations. Let X be any subset of the set of positive integers Z. Define a relation ~ on X as follows: I have reflexive proven, having trouble with transitivity and symmetric. Quessyrutty6w 2022-07-18 Answered
Equivalence Relations (Discrete Math)
I'm having trouble with this math problem on equivalence relations. Let X be any subset of the set of positive integers Z. Define a relation ~ on X as follows:
I have reflexive proven, having trouble with transitivity and symmetric.
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Step 1
Symmetric: If $a/b={2}^{k}$ then $b/a={2}^{-k}$
Step 2
Transitive: If $a/b={2}^{{k}_{1}}$ and $b/c={2}^{{k}_{2}}$ then $a/c=\left(a/b\right)\left(b/c\right)={2}^{{k}_{1}+{k}_{2}}$
###### Not exactly what you’re looking for? phepafalowl
Step 1
Symmetric if: $\frac{a}{b}={2}^{n}$ then what does $\frac{b}{a}$ equall?
Step 2
Transitive: Start by saying what you know
$\frac{a}{b}={2}^{n}$
and $\frac{b}{c}={2}^{k}$