# Thread: Basic Set Theory Question

1. ## Basic Set Theory Question

is |A| + |B| same as |A U B|?
and why if they are not, i see that |AUB| is |A| + |B| - |A n B| (A intersect B)
but why would you need to do that, cause if there are repeated elements then they can't repeat by them self cause sets are distinct elements...

2. Originally Posted by AwesomeDesiKid
is |A| + |B| same as |A U B|?
and why if they are not, i see that |AUB| is |A| + |B| - |A n B| (A intersect B)
but why would you need to do that, cause if there are repeated elements then they can't repeat by them self cause sets are distinct elements...
If $A\cap B\ne\varnothing$ then $\left|A\right|+\left|B\right|$ counts the repeated elements twice.

3. Originally Posted by Drexel28
If $A\cap B\ne\varnothing$ then $\left|A\right|+\left|B\right|$ counts the repeated elements twice.
well, i don't understand the difference between |A XOR B| and |A U B|
xor is exclusive or(you probably know) wouldn't they equal the same thing

4. Originally Posted by AwesomeDesiKid
well, i don't understand the difference between |A XOR B| and |A U B|
xor is exclusive or(you probably know) wouldn't they equal the same thing
My understanding is that $A\text{ XOR }B=A\text{ }\Delta\text{ }B=\left(A-B\right)\cup\left(B-A\right)$. Is that correct?

5. Originally Posted by Drexel28
My understanding is that $A\text{ XOR }B=A\text{ }\Delta\text{ }B=\left(A-B\right)\cup\left(B-A\right)$. Is that correct?
i have no idea what that delta means?

6. Originally Posted by AwesomeDesiKid
i have no idea what that delta means?
Th symmetric difference. I told you want it means after that. In any case, I am moderately sure that I am correct in interpreting what you mean by $A\text{ XOR }B$. Your answer is then $A\cup B=A\text{ XOR }B$ iff $A\cap B=\varnothing$.

7. Originally Posted by Drexel28
Th symmetric difference. I told you want it means after that. In any case, I am moderately sure that I am correct in interpreting what you mean by $A\text{ XOR }B$. Your answer is then $A\cup B=A\text{ XOR }B$ iff $A\cap B=\varnothing$.
i think i got the difference, if |A U B| has all the elements from a and b.
so if A = {0, 1, 2} and B = {1,2,3} then
|A U B| = |0, 1, 2, 3} but
|A XOR B| = {0. 3}
if i m right....... thanks for the help, if not...I HAVE NO HOPE ANYMORE
lol

8. Originally Posted by AwesomeDesiKid
i think i got the difference, if |A U B| has all the elements from a and b.
so if A = {0, 1, 2} and B = {1,2,3} then
|A U B| = |0, 1, 2, 3} but
|A XOR B| = {0. 3}
if i m right....... thanks for the help, if not...I HAVE NO HOPE ANYMORE
lol
! One note though, $\left|\text{some set}\right|$ usually means the cardinality.

9. so A U B DOES equal A XOR B as long as A n B equals phi?