#propositional calculus

[addressingsophism]

Not everything is black and white, nor either-or.

[lawsofemotion]

A blog about mathematics.

Created (1.1) propositional connectives and truth tables!

[anaxerneas]

I have trouble understanding material implication, specifically how "p materially implies q" is true when p is false and q is true. I was wondering if p would simply be irrelevant to q in that case, and the traditional truth tables just don't account for that possibility.

I came across this truth table searching for one on google images. I haven't read the article it's from and the words "defective table" don't inspire much hope, but maybe "indeterminate" is what I had in mind.

Table 1 The Truth Table for a Material Implication p Implies q and the...

Download Table | The Truth Table for a Material Implication p Implies q and the Truth Table Known as Defective for an If p Then q Conditiona

Is it only "defective" by the standards of classical logic?

[anaxerneas]

https://en.wikipedia.org/wiki/Indicative_conditional

Indicative conditional - Wikipedia

[the-decadence]

Hey guys, just wanted to let you know about a cool thing made by professor Terence Tao himself!

As you can see from the screenschot, QED [http://www.math.ucla.edu/~tao/QED/QED.html] is described as an interactive textbook [published on 28th of July so it is in its early phase/new exercises were added as I completed few of those/etc.] and it is great.

You know your girl Nic loves logic, so propositional calculus in a form of a game is a real treat. Now there’s information on how many steps the shortest known proof got, so the competition is on!

But seriously, the idea of learning through play seems quite obvious, but why use it only with younger kids? I’m 21 and I’m having time of my life [at 3:30 AM] while trying to “beat the level” with as few “moves” as I can. Not to mention that this is a great tool for working on “basic higher ed math skills” which consists of writing proofs, using simple concept to create more advanced structures, etc.

More info on professor Tao’s website - https://terrytao.wordpress.com/2018/07/28/gamifying-propositional-logic-qed-an-interactive-textbook/

[raggedinflux]

IF-THEN STATMENT OR CONDITIONAL 3 Relations

Conditional                         If p then q                   p=>q

Converse                            If q then p                   q=>p

Inverse                               If ~p then ~q              ~p=>~q

Contrapositive                  If ~q then ~p              ~p=>~q

[raggedinflux]

Truth Table for a Conditional

P      Q      P->Q

T     T         T

T     F         F

F     T         T

F     F         T

[raggedinflux]

Disjunction - OR - V

In logic, a disjunction is a compound sentence formed by combining two sentences (or facts) using the word "or." A disjunction is true when EITHER or BOTH sentences (or facts) are true.

The logical connector symbol for a disjunction: V