query: Listing equivalence relations class for $x\sim y \Leftrightarrow x^2=y^2$
positive_passages.docid: 98630
positive_passages.text: For all $x,y\in\mathbb{R}$ define that $x\equiv y$ if $x^{2}=y^{2} $; prove $\equiv$ is an equivalence relation.
negative_passages.docid: 136883
negative_passages.text: The class of equivalence.
negative_passages.docid: 59727
negative_passages.text: Understanding equivalence class, equivalence relation, partition
negative_passages.docid: 73334
negative_passages.text: Proving this relation is transitive
negative_passages.docid: 74114
negative_passages.text: How to find the number of anti-symmetric relations?
negative_passages.docid: 138436
negative_passages.text: How to prove reflexivity, symmetry and transitivity for the following relation?
negative_passages.docid: 85713
negative_passages.text: Showing Parallelism is an equivalence relation in $\Bbb R ^2$
negative_passages.docid: 93952
negative_passages.text: Show that $X$ can be represented as a union of disjoint equivalence classes
negative_passages.docid: 109318
negative_passages.text: Equivalence relation $(a,b) R (c,d) \Leftrightarrow a + d = b + c$
negative_passages.docid: 36325
negative_passages.text: Embedding ordinals in $\mathbb{Q}$
negative_passages.docid: 62455
negative_passages.text: Prove Equivalence Relation in G
negative_passages.docid: 110075
negative_passages.text: How to show the given equality
negative_passages.docid: 17363
negative_passages.text: Prove that the intersection of two equivalence relations is an equivalence relation.
negative_passages.docid: 145531
negative_passages.text: relation between first kind Chebyshev poly and second kind Chebyshev poly
negative_passages.docid: 62966
negative_passages.text: Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
negative_passages.docid: 29232
negative_passages.text: Find total number of relations that are equivalence as well as partial order set
negative_passages.docid: 69043
negative_passages.text: The equivalence relation generated by a relation