If A ⊆ B and B ⊆ C then A ⊆ C. Can anyone give a

>>7931318
Anyone who understands what those symbols mean should be able to give a formal proof.

Take x in A, then x is in B, then x is in C, qed

>>7931318

You need to assume transitivity

That's it

>>7931646
>assume transitivity
That's what you're proving.

Isn't this one of de Morgan's laws? I'm forgetting my set theory...

>>7931318
Assuming symmetry and reflexivity has been proven you can use those two properties to prove transitivity. Otherwise the formal proof is a tad long.

>>7931318
>that image
Jesus fucking Christ, murricans.

>>7931318
Yes, anyone can provide a proof of this.

File: 51HwSqLvDSL._SX314_BO1,204,203,200_.jpg (31KB, 316x499px) Image search: [Google]

31KB, 316x499px

pretty sure 1st chapter of this book goes into it

>>7931692

For your homework? No.

>>7931694
don't you worry about my homework

>>7931658
Seriously? (Fuck latex right now, I'm on mobile and you don't deserve it.)
Assume A<B and B<C
Let x in A.
We have two statements: if y in A then Y in B and if y in B then y in C. X in a so x in B. x in B so x in C.

but what happens when you can't get C from A

real-num-fags BTFO

>>7931694
I'm not OP and I'd kill myself if that was my retard homework. Reading comprehension is important, friend.
OP asked if anyone could give a proof.
I said that yes, indeed, any fucking retard can.

>>7931702
>He thinks that transitivity of a relation only occurs in the reals.

>>7931708
> he thinks nonreals and imaginaries are the same
> he never defined the parameters under which A arises
> he still thinks in algebra

>>7931724
srs

>>7931649

You can't prove an axiom

>>7931318
Consider any $x$. Since $A \subseteq B, \forall x \in A \to x \in B$, and since $B \subseteq C, \forall x \in B \to x \in C$. Then, by transitivity of implication, $\forall x \in A \to x \in C$.

>>7931793
Consider any [math] x [/math]. Since [math] A \subseteq B, \forall x \in A \to x \in B [/math], and since [math] B \subseteq C, \forall x \in B \to x \in C [/math]. Then, by transitivity of implication, [math] \forall x \in A \to x \in C [/math].

follows by axiom of extensionality

>>7931803
What if we're using the axiom of choice?

modus ponens, shit stain. Fuggin elementary

Say that every element of A is included in B, and that every element of B is included in C.
In order for A not to be included in C, then there must be some element x in A that is not in C. Let's imagine this element x that isn't in C. We know that every element of A is included in B, so our x not in C is included in B. However, we started by saying that every element of B is included in C, and an element x violates this, so there can not be an element x included in A that is not included in C, so every element of A is in C.

>>7931318
That image can't be true... I don't want it to be

>>7931796
>transitivity of implication
transitivity of implication is encoding of transitivity of the subset relation, your proof is circular

muh dik is inside ur mom's pussy
Your mom's pussy is part of your mom
So muh dik is inside ur mom

>>7933531
Just took my first Fundamentals class in uni for pure math today and I was first introduced to what modus ponens is and fuck me he wasn't even using those symbols. It was with 'and' and 'or' I think. I have it in my notes.

We were doing truth tables and shit, how does that translate to sets?

>>7931318
A subset of B simply means that every element of A is in B. Use that definition and let x be some element of A. I'd maybe use contradiction for this one

Since a is included in b, there exists q ∈ Z such that b = q · a. Similarly, since b is included in c, there exists r ∈ Z
such that c = r · b Thus c = r · (q · a) = (r · q) · a (by associativity) so a is included in c.

>>7931318
Just work backwards.

>>7931646
>transitivity

fucking liberals forcing the gay agenda into math!!!!!

>>7934553
Seriously?

>>7934577
>>>/pol/

>>7931318
>That image
How on Earth did america manage to become the most powerful country on Earth with a population so dumb

>>7936409
America has never been about its population. Its population is kept at sheeple level by consumerism and empty nationalism that encourages its enthusiastic people to apply to get paid to murder people overseas for america's 'greatness' and 'freedom'. The U.S. has always been about its top 1%, these are the people that have made it 'great' through indoctrinating the 99%.

>>7934800
are you mad i proved the unprovable?

>>7931318
>If A ⊆ B and B ⊆ C then A ⊆ C.
false

>>7937310
All you have proven is that you are either a moron or a lousy troll or maybe both.

>set theory
What is the point of this garbage? I'm in calc 3 and haven't used it since algebra 2/pre calc

>>7931658

lol dude

File: 1456840054646.png (112KB, 270x303px) Image search: [Google]

112KB, 270x303px

>>7937384
>calc 3

youve barely done any real mathematics though.