Checking if $p$ tautologically implies $q$

Question

What is the difference between $p\Rightarrow q$ and $p\to q$? Is $p\to q$ a necessary and sufficient condition for checking $p\Rightarrow q$ is a tautology? Are there alternative approaches?

What is $\to$? Is it supposed to be a logical deduction, like $p \vdash q$ ? — DanielV, Jan 24 '16 at 09:21
Twistedly related: http://www.ditext.com/carroll/tortoise.html. — Martín-Blas Pérez Pinilla, Mar 08 '16 at 07:35

score 1 · Answer 1 · answered Mar 08 '16 at 07:03

1

Usually, $\to$ is the conditional (i.e. the connective "if__ ,then __") while "tautologically imples" is denoted with $\vDash$.

The relation between the two is the following:

$p \vDash q$ iff $p \to q$ is a tautology.

answered Mar 08 '16 at 07:03

Mauro ALLEGRANZA

94,169

Checking if $p$ tautologically implies $q$

1 Answers1