How can it be that $(P \rightarrow Q) \vee (Q \rightarrow P)$ is a tautology?
70117
Show that $(p \to q) \lor (q \to p)$ is a tautology
75381
How can we reason about "if P then Q" or "P only if Q" statements in propositional logic?
47161
Quick logic question about $P\leftrightarrow Q$, terminology
63963
deductive system where the axioms are all the propositions that are not tautology
18140
When does $\,n\mid q^3 \Rightarrow n\mid q\,$?
21035
Clarifying on how if p,q is logically equivalent to p only if q
147375
Prove :(P → Q) ∨ (Q → P) using natural deduction
75007
How can I prove this relation between the elementary set theory and the elementary logic?
152297
Understanding quotients of $\mathbb{Q}[x]$
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.
136584
Understanding connection between terms tautology, contradiction, contingent, satisfiable, unsatisfiable, valid and invalid
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
137711
Alternative proof that $[\Bbb{Q}(\zeta_n) : \Bbb{Q} ]= \varphi(n)$ uses circular reasoning?
116978
Trying to prove $p,p \to (r \to q) \vdash (\neg q \to \neg r)$ by using natural deduction.
94771
Not every boolean function is constructed from $\wedge$ (and) and $\vee$ (or)
115726
For $p,q$ prime and $p \neq q$ show that $C_p \times C_q \cong C_{pq}$
48213
proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$