Let $F$ be a field, show that $(A \setminus C) \setminus (B \setminus C) = (A \setminus B) \setminus C\; \forall A, B, C$ in $F$
13136
Element chasing proof that $(A\setminus C)\setminus(B\setminus C) = (A\setminus B)\setminus C$
85096
Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$.
112556
When is $F(\sqrt c)$ a field?
64656
how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
151928
How to prove that $N\setminus A$ is finite?
79061
show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
63280
Show that the set $\mathbb{Q}[\sqrt{2}] = \{a + b \sqrt{2} \mid a, b \in \mathbb{Q}\}$ is a field with the usual multiplication and addition.
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
18126
If $f \colon [a,b] \rightarrow \mathbb{R}$, then show that there exists $c \in [a,b]$ such that $\int_a^c f = \int_c^b f$
129480
Prove that inf(A+B) = infA + infB
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
139841
Proving $A\setminus(B\setminus C)$ is not equal to $(A\setminus B)\setminus C$
97184
Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $
149399
Given continuous $f$ and $g$, there exists $c \in (a,b)$ such that $\int_{a}^{c} f(x) \ \mathrm dx = \int_{c}^{b} g(x) \ \mathrm dx$
123890
Show $A\setminus (A\cap B)=(A\cup B)\setminus B$
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
50655
Proof of $f^{-1}(B_{1}\setminus B_{2}) = f^{-1}(B_{1})\setminus f^{-1}(B_{2})$