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 Post subject: set theory
PostPosted: Sun, 20 Dec 2020 05:13:38 UTC 
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if AUB=A then prove B is the empty set

I started by assuming that \neg (B=\phi)
But i could not get a contradiction


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 Post subject: Re: set theory
PostPosted: Sun, 20 Dec 2020 08:32:24 UTC 
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That is false; one can only show thatA\cup B=A is equivalent to B\subseteq A

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The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low, and achieving our mark. - Michelangelo Buonarroti


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 Post subject: Re: set theory
PostPosted: Sun, 20 Dec 2020 12:26:34 UTC 
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The problem is taken from the book :"SET THEORY AND LOGIC" by ROBERT S. STOLL Page 19


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 Post subject: Re: set theory
PostPosted: Sun, 20 Dec 2020 16:21:40 UTC 
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I don't care. Counterexample: A=\{1,2\},\ B=\{1\}.

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The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low, and achieving our mark. - Michelangelo Buonarroti


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 Post subject: Re: set theory
PostPosted: Mon, 21 Dec 2020 03:11:21 UTC 
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idi wrote:
The problem is taken from the book :"SET THEORY AND LOGIC" by ROBERT S. STOLL Page 19



false problem


Last edited by idi on Mon, 21 Dec 2020 03:36:36 UTC, edited 1 time in total.

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 Post subject: Re: set theory
PostPosted: Mon, 21 Dec 2020 03:28:37 UTC 
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helmut wrote:
That is false; one can only show thatA\cup B=A is equivalent to B\subseteq A


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 Post subject: Re: set theory
PostPosted: Mon, 21 Dec 2020 03:32:26 UTC 
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helmut wrote:
I don't care. Counterexample: A=\{1,2\},\ B=\{1\}.


true


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 Post subject: Re: set theory
PostPosted: Mon, 21 Dec 2020 03:33:34 UTC 
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idi wrote:
helmut wrote:
That is false; one can only show thatA\cup B=A is equivalent to B\subseteq A


true


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