proof that p implies q entails not p or q
87955
How to prove that $P \rightarrow Q$ is equivalent with $\neg P \lor Q $?
19811
$(P(X), C_R)$ may be a choice structure even if $R$ is not a rational relation.
140194
Using natural deduction to prove that $p \implies q \vdash \lnot p \lor q$
32027
Given (p ∧ q), use the Fitch system to prove (q ∨ r)
79407
How to solve ~(P → Q) : P & ~Q by natural deduction?
83407
How to show that that $q \mid p-1$?
87928
Proof of logical equivalence of biconditional and other proposition
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
67709
Stuck with proof for $\forall A\forall B(\mathcal{P}(A)\cup\mathcal{P}(B)=\mathcal{P}(A\cup B)\rightarrow A\subseteq B \vee B\subseteq A)$
14447
Direct proof that $\pi$ is not constructible
93410
How to prove ~ (~P & ~Q) : P ∨ Q by natural deduction
116215
Prove that $P(A \cap B\mid C)=P(A \mid (B \cap C))P(B\mid C)$
110166
If P is a property, then is (not P) a property?
115004
If $x\notin\mathbb Q$, then $\left|x-\frac{p}{q}\right|<\frac{1}{q^2}$ for infinitely many $\frac{p}{q}$?
35370
Why is this proposition provable and its converse not?
148790
Basic question about proofs with the goal $\exists x P(x)$
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.