Showthat $\mathrm p \leftrightarrow \mathrm q$ and $(\mathrm p\wedge \mathrm q) \vee (\neg \mathrm p \wedge \neg \mathrm q)$ are logically equivalent
48213
proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$
58028
Semisimplicity is equivalent to each simple left module is projective?
99911
How to show that if $x=(p,q)$ and $y=(p',q')$ then $x \sim y $ if $pq'=p'q$ is an equivalence relation?
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
32009
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.
88104
Prove "$(p \lor q) \land (\neg p \lor r)) \rightarrow (q \lor r)$" is a tautology
37924
Equivalence of norms proof
91861
Propositional Logic: p → q, ¬p → r, ¬q → ¬r ⊢ q
92492
Natural Deduction: $(p \lor q)\to r\vdash p \to r$ and $p\to\neg q\leftrightarrow(r\lor s),\neg s\vdash (p\land \neg q)\to r$
147375
Prove :(P → Q) ∨ (Q → P) using natural deduction
10540
Prove $\vdash \neg(\square F\land p)$ in $KD$
61066
Prove: $(A\rightarrow B),(A\rightarrow C)\rightarrow B, \mapsto_{HPC} B $
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
25187
Why $∀x(P(x)→Q)$ is equivalent to $∃xP(x)→Q$
127291
Show that $\left( \frac{q}{p} \right) \equiv q^{(p-1) / 2} \mod p$, where $\left( \frac{q}{p} \right)$ is the Legendre Symbol
11342
Show that conguence $\bmod m\,$ is an equivalence relation
132532
Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$