set theory

idi · **Joined:** Fri, 28 May 2010 02:57:26 UTC **Posts:** 108

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

helmut · **Posted:** Sun, 20 Dec 2020 08:32:24 UTC

That is false; one can only show that $A\cup B=A$ is equivalent to $B\subseteq A$

idi · **Joined:** Fri, 28 May 2010 02:57:26 UTC **Posts:** 108

The problem is taken from the book :"SET THEORY AND LOGIC" by ROBERT S. STOLL Page 19

helmut · **Posted:** Sun, 20 Dec 2020 16:21:40 UTC

I don't care. Counterexample: $A=\{1,2\},\ B=\{1\}$ .

idi · **Joined:** Fri, 28 May 2010 02:57:26 UTC **Posts:** 108

idi wrote:

The problem is taken from the book :"SET THEORY AND LOGIC" by ROBERT S. STOLL Page 19

false problem

idi · **Joined:** Fri, 28 May 2010 02:57:26 UTC **Posts:** 108

helmut wrote:

That is false; one can only show that $A\cup B=A$ is equivalent to $B\subseteq A$

idi · **Joined:** Fri, 28 May 2010 02:57:26 UTC **Posts:** 108

helmut wrote:

I don't care. Counterexample: $A=\{1,2\},\ B=\{1\}$ .

true

idi · **Joined:** Fri, 28 May 2010 02:57:26 UTC **Posts:** 108

idi wrote:

helmut wrote:

That is false; one can only show that $A\cup B=A$ is equivalent to $B\subseteq A$

true

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