Logic problem

How would you express "If 1 element in X is false, then all elements in X are false" mathematically/Logically?

assuming you have some set of expressions/variables: in this case you can't have a mix of true and false, so all the expressions in your set are logically equivalent

That's a cool math trick

As for your question, isn't this basically the AND operation?

so p1 p2 .... pn

where {p1...pn} is your set of expressions

Or this too
With AND it would be p1 ^ p2 .... ^ pn - truth condition (all of them have to be true otherwise it's false) stays the same

Actually, yes! But I wanted to express it more mathematically instead of using just words. Also it is a set, so I guess like a function...? Like (∀P(x)) & ... Agh, I guess I don't know how to frase it. Hope you guys get the point

they can all be false, in which case the statement still holds, so it isn't AND.

∀x∈X(¬x→∀y∈X(¬y)) should work

If ∃x∈S s.t. x=0, then ∀x∈S x=0

you don't really need quantifiers/first order logic. again, this is just logical equivalence.

[math](\exists x \in S / \neg x) \implies ( \forall x \in S, \neg x ) [/math]

Is one way to put it, but I also thought of longer ways to put it. You can read it as

If there exists x element of S such that not x is true then for all x element of S, not x is true.

All elements are either false or true

You would write

If there exists an element a in X such that x is false, then all elements in X are false.

and could symbolize that like this

[math]\exists a: a \in X, \neg x \rightarrow \forall a: a \in X, \neg a[/math]

>2 digit numbers
>large

Bin Laden Math

jesus people, you don't need quantifiers to deal with this problem. if your domain of discourse is just a set of propositions, then you can use propositional logic

what does : mean. How could I learn more about logic?

>you don't need quantifiers to deal with this problem

But it looks better with quantifiers. looks better than Plus, is incomplete. It would be more like: X={p1,...pn} is such that p1 p2 .... pn

you're misusing the notation of FOL.

if you want a pretty looking expression:

[math]\wedge_{p,q \in X} p \Leftrightarrow q [/math]

I'd read : as "such that". Though I wrote it wrong, as is it reads "If there exists an a such that a in an element of X and a is not ture, then for every a, a is an element of X and a is not true." Some fiddling will make it read "If there exists an a in X such that not a, then every a in x is not true.

The topic you want to study is formal logic, there are a lot of good introductory books. (Though I find the practice of encoding english into formal logic symbols boring and would instead recommend a discrete mathematics textbook)

>FOL

First order logic is for wimps. I never understood what the problem is with higher order logic.

And that expression is pretty good. I approve.

So how does that work for two wildly different numbers, like

65 x 26?

it's not necessarily wrong to use the language of FOL for this, but it indicates some confusion about what quantifiers are usually used for.

Doesnt this assume that every element of the matrix is an expression? Couldnt the matrix include both expressions and numbers?

there is no matrix involved.

set whatever

for two wildly different numbers you could do 50 or 10
for that I would double 65, times that by 10, then 65*6
so that would be initially 1300
390 is 65*6 (To make it easier just double it then 130*3)
so its 1690
solved in like 5 seconds

for 50, just do by 100 then halve it. using 10s, 50s, and 100s, you can get most things quickly

>Doesnt this assume that every element of the matrix is an expression?

Yeah. You can't "not" things that are not propositions so obviously it is a set of propositions.

>If 1 element in X is false, then all elements in X are false
is not equivalent to
>p1 p2, for all p1, p2 in X
because take the set {True, 2}, clearly True 2

the OP didn't really say, but you can't call it an unreasonable interpretation that each element is either true or false. otherwise, it's a very different question.

give me a break...

exactly, you cant make assumptions that change the context of the statement

yes, yes you can. what kind of retarded question would it be otherwise?

since the OP didn't provide any formal definition/predicate for equality, i think that i'm in the right.

why can't 2 = True? if you discard my original interpretation, then this is also fair game.

>why can't 2 = True?

This is funny because in programming a constant 2 is actually true. Actually, all numbers except for 0 are true.

For example, if you run this program:
#include
#include

int main()
{
if(2) std::cout

/thread