How am I fucking up the Venn Diagram? The two statements are

>>7910705
Why is the graph on a chalkboard white on a black background when on a computer screen or piece of paper, it's black with a white background? Obviously they're opposites...

Math doesn't care about our coordinate systems or methods of drawing it.
The venn diagram has no meaning except what you assign to it. Is shaded 'marked' or is the unshaded 'marked'?
It ultimately depends on how you draw it, and in one, you seem to have done one and the opposite in the other.

>>7910705
Just because two statements are true doesn't mean that they are equal.

>>7910713
I'm using contraption in logic to get from the first statement to the second, they should be logically equivalent.

All non-A are B
(flip subject and predicate)
All B are non-A
(replace with term complements)
All non-B are A

>>7910712
Shading is meant to signify that whatever is shaded is empty.

>>7910729
What's contraption?
Did you mean contrapositive?
In which case you want to check that you're actually using it correctly.

>>7910729
I'm using contraposition**

>>7910734
>Shading is meant to signify that whatever is shaded is empty.

Then it has nothing to do with your logical statements.

>>7910740
I believe I am here
>>7910729
>All non-A are B
(flip subject and predicate)
All B are non-A
(replace with term complements)
All non-B are A

The diagram is showing something else though. They should be identical

>>7910744
How?

All A are B

A would be shaded (empty) except where it is AB, and B would not.

>>7910750
>completely ignoring the first post logically explaining superposition

I hear Starbucks is hiring.

Just for shits and giggles:
Shaded "means" filled and not shaded "means" empty because you defined it. You could easily define shaded to mean empty in one and define shaded to mean full in the other, and they would still look completely opposite.

File: wut.jpg (2MB, 3264x1836px) Image search: [Google]

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>>7910705
You need a universal.
You are shadowing the oval in the middle, that is not correct because elements of that middle area is elements of both A and B.

Also, it does not necessarily mean that there exists a [math]A\cupB[/math] at all.

>>7910789
[math] A \cup B [/math]*

>>7910787
Ok listen. My textbook just gave me that rule to go by, I don't care about the notation and I don't know why you are fixated on it because that is not my problem.

The problem I am having is that these two statements should be logically equivalent without Venn Diagrams, and my textbook says that the Venn Diagrams should follow.

tldr; the problem is they are "opposite", not the meaning of the shading. Go ahead and flip it I dont care.

>>7910789
A \cap B *
fucking...

>>7910800
Read my post
>>7910789

You are shadowing [math]A \cap B [/math] which does not fit your statement.
[math] A \cap B [/math] are elements of both A and B. Mean they are not non-A or non-B. You should rather shadow like i did in upper post.

If there ain't no [math] A \cap B [/math] area, then the circles should be seperate and not share an area.

File: 1449126754049.jpg (42KB, 340x277px) Image search: [Google]

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>>7910789
Even with the shading correction It doesnt line up with what my text says.

Take
All A are B (true)

and the contrapositive of it

All non-B are non-A (true)

If you shade in these Venn Diagrams they are identical.

I was assuming that this is showing the logical equivalence and that similar statements would follow.

So

All non-A are B (true)

contrapositive

All non-B are A (true)

I don't need the Venn Diagrams to know that the contrapositive will have the same truth value as the given statement, I can work that out without one.

I just don't understand why the Venn Diagrams aren't identical like the first example is (All A are B, All non-B are non-A)

File: Mein+Kampf.jpg (354KB, 988x1500px) Image search: [Google]

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>>7910800
>My textbook said it
>I don't need to think about it in any way
>It's true gaiz

>>7910820
That isn't what I said.

>>7910812
IN other words, if your two statements are true
Then

[math] A \cap B = \varnothing [/math]

File: wut2.jpg (1MB, 3264x1836px) Image search: [Google]

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>>7910819
this guy again >>7910829

I don't understand what you are saying.
You do know that all non-B does not have to be an element of A? A non-B can be an element of another set, not just A.

>>7910852
Yes I got my mistake with the shading, thanks for that.

The confusion I'm having is this. My textbook is going over categorical propositions for logic. It goes over given statements that have a truth value, how a relation changes it, and then gives the new statement with the new truth value. Certain relations have certain properties. They then showed the patterns that the relations have via Venn Diagrams. They flat out say what the relations do to the truth value of the new statement, and they also show it through Venn Diagrams.

I can follow the statements without the Venn Diagrams, but with them it trips me up.

Sometimes Contrapositive is supposed to give the same truth value is was given (Given statement is true, new statement must also be true). My OP example is this. The given statement is true, the new statement is true.

This should be illustrated through a Venn Diagram (I thought), where the first statement and the new statement should be identical.

>>7910820
Why'd you post Mein Kampf? The Communist Manifesto would have been more fitting.

>>7910885
But.. doesn't the venn diagram in this post >>7910852
show it?

You have gotten me interested aswell because I am starting to doubt my knowledge in logic.

Both OP and >>7910852 drew the wrong venn diagrams.

The Venn diagrams for either statement looks like this:

Two circles, A and B, overlapping, with [math] A \cup B [/math] shaded in. All that's necessary is that there is nothing in the complement of [math] A \cup B [/math].

Another way to see this is that "all non-A are B" is equivalent to " [math] \lnot A \rightarrow B [/math] ".

[math] p \rightarrow q [/math] is logically equivalent to [math] \lnot p \vee q [/math].

Thus, "all non-A are B" is equivalent to " [math] \lnot A \rightarrow B [/math] " is equivalent to [math] \lnot \lnot A \vee B [/math] is equivalent to [math] A \vee B [/math].

Shade both A and B in the Venn diagram.

>>7910903
Thank you sir.

ps not op

>>7910903
Fucking thank you. I can't completely follow your explanation because of the notation but once I saw the Venn Diagram it was right. Still..I can't really explain it to myself which pisses me off.

>>7910900
And thank you too

>>7910705

First of all, the convention is that you shade the one that's full, and the empty one is empty

Now, why are you shading only A (look at the first one, the 2nd one is just the contrapositive)
It says: If not A, then B.
It doesn't say: Only A

What "If not A, then B" means: If it's not in A, then it must be in B. The only way this is false is if there is something that isn't in A and also isn't in B. That means you can't have anything outside the circles. Shade everything else.

>>7910926

see >>7910934

If it's not in A then it is in B

It doesn't say it can't be in A. So shade A.

It doesn't say it can't be in both. So shade the middle

It doesn't say it can't be in B. So shade B

It says that if it sin't in A, then it is in B. This means that everything is either in A or B, because if it's not in A, it's in B. The only thing that's being excluded is the outside of both circles. Draw your circles in a box to represent this.

>>7910939

The V means "or"

Upside down V means "and"

"if" ---> "then"

<---> biconditional obviously

>>7910943
Gotcha, and with the notation my textbook goes with, everything outside the union would be shaded with everything inside the union empty.

Thanks