query: Short Prove or Disprove: $R_1 \cap R_2$ is an equivalence relation
positive_passages.docid: 17363
positive_passages.text: Prove that the intersection of two equivalence relations is an equivalence relation.
negative_passages.docid: 75387
negative_passages.text: A proof that $1=2$. May I know why it’s false?
negative_passages.docid: 83475
negative_passages.text: Prove Or Disprove: tr(AB)=tr(A)*tr(B)
negative_passages.docid: 13415
negative_passages.text: How to show if $A \subseteq B$, then $A \cap B = A$?
negative_passages.docid: 52135
negative_passages.text: Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
negative_passages.docid: 43310
negative_passages.text: Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
negative_passages.docid: 77757
negative_passages.text: Infer the second isomorphism theorem from the first one
negative_passages.docid: 70193
negative_passages.text: Show that the relation defined on an integral domain by "$x\sim y$" ("$x$ is associated with $y$") is a relation of equivalence.
negative_passages.docid: 75863
negative_passages.text: how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
negative_passages.docid: 68014
negative_passages.text: Prove that $\mathfrak{su}(2)$ is not isomorphic to $\mathfrak{sl}(2,\mathbb R)$
negative_passages.docid: 127491
negative_passages.text: Isometric isomorphism between $R^2$ and $R$
negative_passages.docid: 99911
negative_passages.text: How to show that if $x=(p,q)$ and $y=(p',q')$ then $x \sim y $ if $pq'=p'q$ is an equivalence relation?
negative_passages.docid: 85713
negative_passages.text: Showing Parallelism is an equivalence relation in $\Bbb R ^2$
negative_passages.docid: 98518
negative_passages.text: Cardinality of equivalence relations on N
negative_passages.docid: 71977
negative_passages.text: Give an example of a relation R on $A^2$ which is reflexive, symmetric, and not transitive
negative_passages.docid: 65977
negative_passages.text: Showing function is injective iff $f(M_1 \cap M_2) = f(M_1)\cap f(M_2)$
negative_passages.docid: 98630
negative_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.