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Need to check proof of De Morgan's law

  • #1
911
18

Homework Statement



Hi

I have done the proof, just need to check it. I wanted to prove that

[itex]
A\cap B=A\setminus(A\setminus B)
[/itex]

Homework Equations



Proof:

The Attempt at a Solution



[itex]
\mbox{let}\ x\in A\cap B\ \mbox{be arbitrary}
[/itex]
[itex]
\Rightarrow x \in A\ \mbox{and}\ x \in B
[/itex]
[itex]
\Rightarrow x \in A\ \mbox{and}\ x \notin B^{c}
[/itex]
[itex]
\Rightarrow x \in A\ \mbox{and}\ x \notin A\setminus B
[/itex]
[itex]
\Rightarrow x \in A\setminus (A\setminus B)
[/itex]

I know that I have to do reverse proof too. But is it ok so far ?

Thanks
 

Answers and Replies

  • #2
352
0
This is correct so far as it goes, yes.
 

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