Prove that $ \ \forall x \exists y \ P(x,y) \ $ and $ \ \exists y \forall x \ P(x,y) \ $ are not equivalent
5293
Show that the logic $ \ \forall x \exists y \ P(x,y) \ $ is not logically equivalent to $ \ \exists x \forall y \ P(x,y) \ $
140194
Using natural deduction to prove that $p \implies q \vdash \lnot p \lor q$
120252
Equivalences of bounded sets definitions
88736
How does the Axiom of Extensionality prove the uniqueness of Specified sets?
23125
Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
126698
measurability of a function -equivalent conditions
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
82771
Proving that any polynomial $p:\mathbb{R}\rightarrow \mathbb{R}$ is not bounded, but its restriction to any bounded set is bounded
140988
Prove $\exp(x)\exp(y)=\exp(y)\exp(x)$ if $[x,y]=0$.
31392
Examples and Counterexamples of Relations which Satisfy Certain Properties
126633
Is a contradiction enough to prove a set equality to $\varnothing$?
48213
proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$
153634
A statment about the equivalence between the Axiom of Choice and the surjectivity of the projections.
130998
Is $\exists x \in A ~:~ P(x)$ the same as $\exists x ~:~ x \in A \implies P(x)$
59187
Proof, is $\forall x : (P(x) \lor Q(x)) \Leftrightarrow \forall x : P(x) \lor \forall x : Q(x)$?
108367
proving tautologically equivalent
156679
$K[X,Y]/(XY-1)$ not isomorphic to $K[T]$