prove that $f(A) \backslash f(B) \subseteq f(A\backslash B)$
1821
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
7858
Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
113411
If $E$ is generated by $E_1$ and $E_2$, then $[E:F]\leq [E_1:F][E_2:F]$?
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
132971
Prove that $|a| < b \iff -b<a<b$
40604
Is this proof correct for : Does $F(A)\cap F(B)\subseteq F(A\cap B) $ for all functions $F$?
63146
Proof of properties of injective and surjective functions.
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
61640
Prove c exists for f:[0,1] -> R
93157
If $A \subseteq B$, does $\mbox{dist}(x,\partial A) \le \mbox{dist}(x, \partial B)$ hold for all $x \in A$
144693
Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
78463
Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
93102
prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$
80916
How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?
116056
Prove that $|f(x)-f(y)|\le|x-y|$ for all $x$ and $y$.
36093
Show rigorously that the sum of integrals of $f$ and of its inverse is $bf(b)-af(a)$