If B and C are subsets of Y, then prove $f^{-1}(C/B)=f^{-1}(C)/f^{-1}(B)$
6098
Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$
88928
$F:G\to B$ is an isomorphism between groups implies $F^{-1}$ is an isomorphism
51321
Prove that $A = B = C = D$
25258
Prove that if $ a,b,c > 0 $, then $ [(1 + a) (1 + b) (1 + c)]^{7} > 7^{7} (a^{4} b^{4} c^{4}) $.
23869
Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive
76610
Show that $f^{-1}(A \cup B) = f^{-1}(A) \cup f^{-1}(B)$
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
132971
Prove that $|a| < b \iff -b<a<b$
109778
Proving $(x-c)|(p(x)-p(c))$
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
54380
Prove if $|z| < 1$ and $ |w| < 1$, then $|1-zw^*| \neq 0$ and $| {{z-w} \over {1-zw^*}}| < 1$
151038
How to prove (A v B), (A → C), (B → D) therefore (C v D)
70307
$(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
10024
How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$