Why do $\exists x\in S: p(x)$ and $\forall x\in S: p(x)$ have different logical structures?
130998
Is $\exists x \in A ~:~ P(x)$ the same as $\exists x ~:~ x \in A \implies P(x)$
132532
Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
88736
How does the Axiom of Extensionality prove the uniqueness of Specified sets?
94421
Why $P(A) \cup P(B)$ is not equivalent to $P(A \cup B)$
5313
Existence of how many sets is asserted by the axiom of choice in this case?
113861
Exist vs exists in mathematics
91861
Propositional Logic: p → q, ¬p → r, ¬q → ¬r ⊢ q
35123
How do the separation axioms follow from the replacement axioms?
83714
$A \in B$ vs. $A \subset B$ for proofs
75381
How can we reason about "if P then Q" or "P only if Q" statements in propositional logic?
93157
If $A \subseteq B$, does $\mbox{dist}(x,\partial A) \le \mbox{dist}(x, \partial B)$ hold for all $x \in A$
43462
Disprove $\mathcal{P}(A\Delta B) \setminus \{\emptyset\} = \mathcal{P}(A) \Delta\mathcal{P}(B) $. Is my proof good?
113735
Do we need to prove that if x∉A in proposition "if A⊆B then A⋃B=B"?
130865
Why is the axiom of choice separated from the other axioms?
93557
Intuitively, why does (B → S) ≡ (¬B ∨ S)?
152856
Using $p\supset q$ instead of $p\implies q$
29755
Power set equivalency of Axiom of Choice