Set Theory Proof

  • Thread starter cmajor47
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  • #1
cmajor47
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Homework Statement


For all sets A and B, if A [tex]\subseteq[/tex] B then Bc [tex]\subseteq[/tex] Ac.


Homework Equations





The Attempt at a Solution


Proof: Suppose A and B are sets and A [tex]\subseteq[/tex] B.
Let x [tex]\in[/tex] Bc
By definition of complement, if x [tex]\in[/tex] Bc then x [tex]\notin[/tex] B
Since x [tex]\notin[/tex] B, x [tex]\notin[/tex] A
Since x [tex]\notin[/tex] A, x [tex]\in[/tex] Ac by definition of complement
Therefore if A [tex]\subseteq[/tex] B then Bc [tex]\subseteq[/tex] Ac.

I just want to make sure that this proof is correct and that there are no mistakes. Thanks!
 

Answers and Replies

  • #2
Dick
Science Advisor
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It's fine. You might want to enhance it's proofiness by stating the reason why x not in B implies x not in A as you gave a reason for the other lines.
 

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