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Prove that:

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bob bundy****Moderator**- Registered: 2010-06-20
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Looks to me like you have 'proved' it with the diagrams. All you need to do is convert that into set statements and it is done.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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What are set statements?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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Sorry, it is supposed to be This:

Prove that:

I can figure it out myself if you can explain how to get the third line fromt the second

*Last edited by Agnishom (2014-05-01 22:47:05)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bob bundy****Moderator**- Registered: 2010-06-20
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Hmmm. I'm getting Nehushtan's result too, using your definition:

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bob bundy****Moderator**- Registered: 2010-06-20
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Ah! just seen your correction. Revised version coming up.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bob bundy****Moderator**- Registered: 2010-06-20
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Bob

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Nehushtan,

I see it all. The problem seems to be with the proof.

Please Tell me how I can show

bob,

Sorry, I do not get it.

*Last edited by Agnishom (2014-05-01 22:58:14)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bob bundy****Moderator**- Registered: 2010-06-20
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Oh.

line 1: I used your definition for the triangly thing.

line 2: I simplified it. Couldn't make a dash work as in A-dash = not A so I used a wobbly over tilde thingy.

phi is the empty set.

As for this:

Use the distributivity laws

In A AND in the union = just A

Bob

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What did you simplify in line 2? How is this relevant?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bob bundy****Moderator**- Registered: 2010-06-20
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I'll try it in more detail:

So A big triangled with the intersection is (A less the intersection) united with (the intersection less A)

A less the intersection is the bits of A without the bits in B.

The intersection without A is nothing at all so the empty set.

Unite these.

But everything in a set plus the empty set is still just that set so

This is just the definition of \, hence

Bob

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Agnishom wrote:

Please Tell me how I can show

Note that is a subset of . In general, if then .

Proof:

We must prove that both

and . is clear since is a subset of .To prove the other inclusion, suppose

and let . . If we are done. If then, since , we have as well. In either case . Hence .**161** books currently added on Goodreads

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Hmm..

Thanks,

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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