# Tag Info

Accepted

### Why do logic gates behave the way they do?

As stated by user120366, 16 possible 2-input logic gates exist, I've tabulated them for you here: ...

### Why is $A \lor (A \land \neg B) \equiv A$?

I find pictures are great for anything simple enough to use them, which this is. Remember: AND means the area taken up by both things. So the middle one is what is taken up outside B, but also ...

### Why is $A \lor (A \land \neg B) \equiv A$?

There are many ways to see this. One is a truth table. Another is to use the distributive rule:  A \lor (A \land \lnot B) = (A \land \top) \lor (A \land \lnot B) = A \land (\top \lor \lnot B) = A \...

### Why is A implies B true if A is false and B is false?

Humans are bad at logic until they have to employ it to figure out human affairs. Think of "if $A$ then $B$" as a kind of promise: "I promise to you that if you do $A$ then I will do $B$". Such a ...

### What exactly is a logic?

Fundamentally, a logic consists of two things. Syntax is a set of rules that determine what is and is not a formula. Semantics is a set of rules that determine what formulae are "true" and what are "...

### Could Gödel’s incompleteness theorem be circumvented with a quine?

Here is the proof of Gödel's incompleteness theorem, in a nutshell, for a theory $T$. We construct a sentence $\Pi$ which states that "$T$ proves that $\Pi$ is false". The sentence mentions ...