query: For every element $x$ in a given set $A$, $x$ is an element of the corresponding equivalence class $[x]_R$ with R an equivalence relation. Why?
positive_passages.docid: 158009
positive_passages.text: Why is it always the case that, given an equivalence relation R on a set X and a $x \in X$, that x is equivalent to itself?
negative_passages.docid: 87265
negative_passages.text: If $(A-\lambda{I})$ is $\lambda$-equivalent to $(B-\lambda{I})$ then $A$ is similar to $B$
negative_passages.docid: 32180
negative_passages.text: Why is "$A$ unless $B$" equivalent to $A \lor B$?
negative_passages.docid: 84397
negative_passages.text: $x$ conjugate to $y$ in a group $G$ is an equivalence relation on $G$
negative_passages.docid: 131946
negative_passages.text: Order of an Element Under a Homomorphism
negative_passages.docid: 87830
negative_passages.text: Relating the union of the power set of a set to the set itself
negative_passages.docid: 85507
negative_passages.text: Equivalence Relation problem
negative_passages.docid: 25187
negative_passages.text: Why $∀x(P(x)→Q)$ is equivalent to $∃xP(x)→Q$
negative_passages.docid: 46056
negative_passages.text: If $\mathcal{E}$ are subsets of $X$ and $A \subset X$. Show that $\mathcal{A}\mathcal{(E \cap}$ A)=$\mathcal{A}\mathcal{(E)} \cap$ A
negative_passages.docid: 53915
negative_passages.text: prove that $a \equiv b \mod m$ is an equivalence relation on the integers
negative_passages.docid: 77791
negative_passages.text: Proving an inclusion related to algebraic sets and interpreting it
negative_passages.docid: 109054
negative_passages.text: Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?
negative_passages.docid: 110464
negative_passages.text: Let $A=\{1,...,n\}.$ Show that there is a bijection of $P(A)$ with the cartesian product $X^n$ where $X$ is the two element set $X=\{0,1\}$
negative_passages.docid: 104987
negative_passages.text: Equivalence Relation with dividing x and y integers
negative_passages.docid: 144181
negative_passages.text: Given an arbitrary set $X$, can one always find an element outside $X$?
negative_passages.docid: 97801
negative_passages.text: If $R_{1}$ and $R_{2}$ are relations on a set S with $R_{1};R_{2}=R_{2};R_{1}$. Then $R_{1}$ and $R_{2}$ are bijective maps
negative_passages.docid: 136883
negative_passages.text: The class of equivalence.