Show equivalence of statement $\left(P\rightarrow Q\right) \wedge \left(Q\rightarrow R\right)$ to ...
139064
Show by using logical connectives laws that $(P\to Q) \land (Q \to R) $ is equivalent to $(P \to R) \land [(P \iff Q) \lor (R \iff Q)]$
25187
Why $∀x(P(x)→Q)$ is equivalent to $∃xP(x)→Q$
108367
proving tautologically equivalent
21035
Clarifying on how if p,q is logically equivalent to p only if q
59187
Proof, is $\forall x : (P(x) \lor Q(x)) \Leftrightarrow \forall x : P(x) \lor \forall x : Q(x)$?
116978
Trying to prove $p,p \to (r \to q) \vdash (\neg q \to \neg r)$ by using natural deduction.
93342
Show that $\neg$ and $\wedge$ form a functionally complete collection of logical operators.
87265
If $(A-\lambda{I})$ is $\lambda$-equivalent to $(B-\lambda{I})$ then $A$ is similar to $B$
93707
Formal proof for $q \land \neg q \vdash r \land \neg r$
108045
Show that are logically equivalent
134384
What does $\rightarrow$ mean in $p \rightarrow q$
132532
Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
6359
How to know when to use $P(x)\wedge Q(x)$ and when to use $P(x)\to Q(x)$?
41846
$(\mathbb{R}^n,\|\cdot\|_{p})$ is isometrically isomorphic to $(\mathbb{R}^n,\|\cdot\|_{q})$ iff $p=q,$
73526
The equivalence of "Every surjection has a right inverse" and the Axiom of Choice
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
61066
Prove: $(A\rightarrow B),(A\rightarrow C)\rightarrow B, \mapsto_{HPC} B $