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# Set theoretical proof Watch

1. Let and be sets such that . Prove that . [6 marks]

I'm not really sure how to go about answering questions of this type, so excuse how potentially stupid my approach may look.

Proof: Suppose that and such that . Then and . We have that and . But since , we have that and . This then forces the condition that . So So that .
2. (Original post by Zacken)
Proof: Suppose that and such that . Then and .
I don't see how that (final quoted sentence) follows from your definition of x and y.
3. (Original post by ghostwalker)
I don't see how that (final quoted sentence) follows from your definition of x and y.
I was thinking of something along the lines of and but and
4. (Original post by Zacken)
Let and be sets such that . Prove that . [6 marks]

I'm not really sure how to go about answering questions of this type, so excuse how potentially stupid my approach may look.

Proof: Suppose that and such that . Then and .
This doesn't seem to make sense. What stops ? This has to be true for some elements of .

You need to show that:

1.
2.

using the fact that
5. (Original post by Zacken)
I was thinking of something along the lines of and but and
Those are specific elements which wouldn't necessarily be members of general sets. There are no specific elements you can use for a general set.

atsruser's suggestion would be the way I'd do it.
6. (Original post by atsruser)
This doesn't seem to make sense. What stops ? This has to be true for some elements of .

You need to show that:

1.
2.

using the fact that
I see, yeah. That was a bit of a stupid assumption on my part.

Would this be better?

Let , then it follow that , this implies that , so and .

Let , then it follow that , this implies that , so and .

Which shows that and .

Hence .
7. (Original post by ghostwalker)
Those are specific elements which wouldn't necessarily be members of general sets. There are no specific elements you can use for a general set.

atsruser's suggestion would be the way I'd do it.
Yeah, that was a bit of a brain fart on my part. Thanks!
Is my revised proof better?
8. (Original post by Zacken)
I see, yeah. That was a bit of a stupid assumption on my part.

Would this be better?
Yes, that's correct.

BTW you don't need the brackets around the and so on. They're distracting.
9. (Original post by atsruser)
Yes, that's correct.

BTW you don't need the brackets around the and so on. They're distracting.
Yay! Great, thanks to you and Ghost. +Rep.

Right, brackets. Will keep in mind next time!

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