General proof R intersection $R^{-1}$ is an equivalence relation on $X$.
15312
Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
1932
How to show this equality of $\rho(X,Y)$
69043
The equivalence relation generated by a relation
19838
Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
86054
$r+r^{-1}$ integral implies $r^n+r^{-n}$ integral
158009
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?
33030
Proof that $\inf A = -\sup(-A)$
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
10024
How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)
23224
$\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$
87848
Formal proof for $(-1) \times (-1) = 1$
60140
Proof of Equivalence Relation $R=\{(a,b)\in\Bbb N^2: 5\mid (2a+3b)\}$
74311
Proving that the Intersection of any Collection of Compact Sets is Compact
67234
The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
75863
how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$