If I have ((A ∩ B) ∪ Ω), is that equivalent to Ω ?

2. ## Re: Question about sets

Originally Posted by Nombredor
If I have ((A ∩ B) ∪ Ω), is that equivalent to Ω ?
Well of course, if $X\subset Y$ then $X\cup Y=Y~.$
All set are subsets of $\Omega$.

3. ## Re: Question about sets

And I am right in saying that (A -B) ∪ (B - A) is equivalent to (A ∪ B) - (A ∩ B) ?

And is it accurate to say that (A ∩ Ω) ∪ ~B is the same as Ω - B ?

4. ## Re: Question about sets

Originally Posted by Nombredor
And I am right in saying that (A -B) ∪ (B - A) is equivalent to (A ∪ B) - (A ∩ B) ?
That is correct.

Originally Posted by Nombredor
And And is it accurate to say that (A ∩ Ω) ∪ ~B is the same as Ω - B ?
If ~B means $B^c$, the complement of $B$ then no.
$(A\cap\Omega )\cup B^c=A\cup B^c$ which is not necessarily $B^c~.$

5. ## Re: Question about sets

~B means ''non B'' in this case.

6. ## Re: Question about sets

Originally Posted by Nombredor
~B means ''non B'' in this case.
"non B" is not a set theory term.
B complement is the set of all elements not in B.

7. ## Re: Question about sets

Originally Posted by Plato
$(A\cap\Omega )\cup B^c=A\cup B^c$ which is not necessarily $B^c~.$
How do they look different on a Venn diagram ?

8. ## Re: Question about sets

Also, I was wondering whether I was right in saying that (A ∪ B) ∩ (A ∪ ~B) is equivalent to (A - B) ?

9. ## Re: Question about sets

The only thing I've ever seen big-omega used for in set theory is as another name for omega-1 (first uncountable ordinal). Does it also mean "universal set" in the context of intro set theory, then?

10. ## Re: Question about sets

Originally Posted by Annatala
Does it also mean "universal set" in the context of intro set theory, then?
Yes, that's what I meant it as. I've also seen people use just ''u'', but I prefer omega because ''u'' also looks a lot like the reunion symbol.

double post

12. ## Re: Question about sets

Originally Posted by Nombredor
Also, I was wondering whether I was right in saying that (A ∪ B) ∩ (A ∪ ~B) is equivalent to (A - B) ?
it is correct

13. ## Re: Question about sets

Originally Posted by Nombredor
Also, I was wondering whether I was right in saying that (A ∪ B) ∩ (A ∪ ~B) is equivalent to (A - B) ?
No that is not correct.
Let $\Omega =\{1,2,3,4,5,6,7,8,9\},~A=\{1,2,3,4\}~\&~B=\{2,4,6 ,8\}$.

Find $(A\cup B)~\&~(A\cup B^c)$.

What is their intersection? What is $A-B~?$

14. ## Re: Question about sets

it is equal to A

15. ## Re: Question about sets

Originally Posted by Amer
it is equal to A
Correct. So the OP
Originally Posted by Nombredor
I was right in saying that
(A ∪ B) ∩ (A ∪ ~B) is equivalent to (A - B) ?
Is incorrect.

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