query: Why this is true?$\exists x \in U, [P(x) \land Q(x)] \Leftrightarrow [(\exists x \in U, P(x)) \land (\exists x \in U, Q(x))]$
positive_passages.docid: 88281
positive_passages.text: Mixing and Distributing Qualifiers ($\forall x$, $\exists x$)
negative_passages.docid: 137494
negative_passages.text: Why is "If ψ ∈ Γ then the sequent (Γ ⊢ ψ) is correct" true?
negative_passages.docid: 52585
negative_passages.text: How to prove that $[(p \to q) \land (q \to r)] \to (p \to r)$ is a tautology without using the truth table?
negative_passages.docid: 146188
negative_passages.text: Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?
negative_passages.docid: 6119
negative_passages.text: If both $P$ and $Q$ are true , how can I tell that $P$ implies $Q$?
negative_passages.docid: 119888
negative_passages.text: Is it possible to convert $\forall$ quantifiers to $\exists$ quantifiers without negation?
negative_passages.docid: 53101
negative_passages.text: Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
negative_passages.docid: 6535
negative_passages.text: Proof of for-all / there-exists "negation"?
negative_passages.docid: 45481
negative_passages.text: Prove or disprove validity: $(\forall x \exists y (P(x) \supset Q(y))) \supset(\exists y \forall x (P (x) \supset Q(y)))$
negative_passages.docid: 87955
negative_passages.text: How to prove that $P \rightarrow Q$ is equivalent with $\neg P \lor Q $?
negative_passages.docid: 48213
negative_passages.text: proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$
negative_passages.docid: 32009
negative_passages.text: Prove $\;\big((p\rightarrow q) \lor (p \rightarrow r)\big) \rightarrow (q\lor r)\equiv p \lor q \lor r$ without use of a truth table.
negative_passages.docid: 89429
negative_passages.text: Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $
negative_passages.docid: 100399
negative_passages.text: A doubt with a part of a certain proof.
negative_passages.docid: 142762
negative_passages.text: how to prove that (P⊃Q)≡(¬Q⊃¬P) ( P ⊃ Q ) ≡ ( ¬ Q ⊃ ¬ P ) is disallowed in intuitionistic logic?
negative_passages.docid: 48368
negative_passages.text: Prove using Natural Deduction in predicate logic $(\forall x\ P(x))\to Q ⊢ \exists x (P(x)\to Q)$
negative_passages.docid: 34154
negative_passages.text: Prove the statement $\forall x\in\mathbb N (x > 1\to\exists k\in\mathbb N\exists m \in\mathbb N (m \equiv 1 (\text{mod }2) \wedge x = 2^km))$.