Question

If A=B, then AnB=AuB

Answer 1

ok... and? :)

Answer 2

Welcome to Open Study, by the way! :)

What's the question? are you supposed to prove this?

Answer 3

That it does always, never, or sometimes?

Answer 4

Ah, ok... well, what do you think?

Answer 5

It's kind of hard to Venn diagram it, since A=B are just the same circle, right?

so if A=B then everything that's in A is in B, and everything that's in B is in A (there is no difference between the 2, no elements in 1 that aren't in the other).

so what does that mean for the union?

What does that mean for the intersection?

Answer 6

Not sure. Isn't that if A=B then AnB=B and AuB=B, so is it never?

Answer 7

welll.....

But the question is:

Does A=B imply that AnB=AuB?

You just said that A=B implies that AnB=B and AuB=B... which I'll agree with.....

So, DOES it mean that AnB=AuB?

Answer 8

By the way, A=B also implies that AnB=A and AuB=A.

Remember, they are the SAME sets.

Answer 9

So it is always?

Answer 10

Think about what it MEANS, that A=B.... don't just try to "fit" this into some rule you've already learned.

A=B means they have EXACTLY the same elements.

So what's in A{intersect}B ?? Everything that is BOTH sets, right?

What in A{union}B ?? Everything that is in EITHER set, right?

Well, THEY ARE THE SAME SETS. So, isn't everything that's in BOTH, also in EITHER?

Answer 11

Yes, I would think always. Because they are the same sets, so every element that is in EITHER set, it in BOTH sets.

And every element in BOTH sets is in EITHER set.

They are the same. :)

Answer 12

I know intersections are the same numbers that they have in common and and union is of all the numbers combined but not repeated.

Answer 13

Try a few examples to convince yourself... that doesn't PROVE it, but it will help you gain intuition.

A={1,3,5,7,8}, .B={1,3,5,7,8}

What's the union? what's the intersection?

See what I mean? :)

Answer 14

The union is {1,3,5,7,8} and so if the intersection. Right?

Answer 15

*is

Answer 16

Right...


Now, imagine that picture if A=B... the circles "slide" over so that they are exactly on top of each other (the sets are the same).

Think about what happens to the intersection area, and the union area. BOTH just become identical to the circle.