$A$ is similar to $B$ in $E$ if only if $A$ is similar to $B$ in $F$.
57515
Similar matrices and field extensions
13415
How to show if $A \subseteq B$, then $A \cap B = A$?
103801
$xT=x$ iff $x=e$ implies that every $g$ may be written as $x^{-1}(xT)$ for some $x\in G$.
108045
Show that are logically equivalent
25710
$A ⊂ B$ if and only if $A − B = ∅$
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
662
If $E[X|Y]=Y$ almost surely and $E[Y|X]=X$ almost surely then $X=Y$ almost surely
50939
If $A$ and $B$ are nonempty sets, prove that $A \times B = B \times A$ if and only if $A = B$
104424
If each eigenvalueof $A$ is either $+1$ or $-1$ $ \Rightarrow$ $A$ is similar to ${A^{ - 1}}$
125043
Show that F(A−B) is not necessarily a subset of F(A)−F(B).
43059
Show that $g^k=e$ if and only if the order of $g$ is finite and divides $k$.
123555
Proving that if $ab=e$ then $ba=e$
111406
Proving that a definition of e is unique
62770
Does $a\mid bc$ imply $a\mid b$ or $a\mid c$?
53101
Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
134071
If A is a finite set and B is an infinite set, then B\A is an infinite set