show that $(p \to q) \vee (p \to r) \to (q \vee r)$ and $p\vee q\vee r$ are logically equivalent
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.
92492
Natural Deduction: $(p \lor q)\to r\vdash p \to r$ and $p\to\neg q\leftrightarrow(r\lor s),\neg s\vdash (p\land \neg q)\to r$
21035
Clarifying on how if p,q is logically equivalent to p only if q
70409
Rational Equivalence Relation and Measure
53915
prove that $a \equiv b \mod m$ is an equivalence relation on the integers
31299
Using the Fitch system, how do I prove $((p \implies q) \implies p)\implies p$?
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
9282
Prove using natural deduction $((P \land Q) \rightarrow R) \vdash (P \rightarrow R) \lor (Q\rightarrow R)$
56351
Prove that these statements $(A \lor \neg B)$ and $\neg A \to \neg B$ are logically equivalent
121361
Showing that $\lnot Q \lor (\lnot Q \land R) = \lnot Q$ without a truth table
152856
Using $p\supset q$ instead of $p\implies q$
32027
Given (p ∧ q), use the Fitch system to prove (q ∨ r)
59187
Proof, is $\forall x : (P(x) \lor Q(x)) \Leftrightarrow \forall x : P(x) \lor \forall x : Q(x)$?
62455
Prove Equivalence Relation in G
93342
Show that $\neg$ and $\wedge$ form a functionally complete collection of logical operators.
73526
The equivalence of "Every surjection has a right inverse" and the Axiom of Choice