How to prove: $\exists x P(x) \implies Q(y) \Longleftrightarrow \forall x [P(x) \implies P(y)]$
132532
Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
106401
Prove: $p-mq | f(m)$ where $m$ is any integer
59724
Proving that $x_n\to L$ implies $|x_n|\to |L|$, and what about the converse?
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 $p \implies q \vdash \lnot p \lor q$
48213
proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$
50273
How to prove $\lvert \lVert x \rVert - \lVert y \rVert \rvert \overset{\heartsuit}{\leq} \lVert x-y \rVert$?
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
87955
How to prove that $P \rightarrow Q$ is equivalent with $\neg P \lor Q $?
47161
Quick logic question about $P\leftrightarrow Q$, terminology
38785
Prove previsibility and $E[X_{T \wedge n}] \le E[X_{S \wedge n}]$
76347
Shorter proof for some equvalences
83665
Prove a assertion concerning Lebesgue space
34768
Proving $(p \oplus q) \oplus r=p \oplus (q \oplus r)$
129584
How prove $E|X|^p<\infty$ and $E|Y|^p<\infty$, if $E|X+Y|^p<\infty$
148585
Show that, for any $\epsilon>0$, there exist two rationals such that $q < x < q'$ and $|q-q'|<\epsilon$