Math Is Fun Forum

Jassim

Guest

prove that

hi everybody ... please help me in solving this Q :

prove that if B ^ E = Ø and C U B = universal set and A ^ C = Ø then A ^ E = Ø .

note :
^ : intersetion
U : union

thanks in advance

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: prove that

Go by way of contradiction.  Assume that there is an element in both A and E.  Show that this means either B ^ E or A ^ C is non-empty.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: prove that

If X ^ Y = Ø, then X and Y have no common elements. Another way of thinking about this is that if an element in in X, then it can't be in Y.

If X U Y is the universal set, then X and Y between them have every element. In other words, if an element is not in X, then it must be in Y.

Now consider an element in A.
This element is not in C, because A ^ C = Ø.
Therefore, it is in B, because C U B = universal set.
Therefore, it is not in E, because B ^ E = Ø.

No element of A can be in E, and hence A ^ E = Ø.

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Why did the vector cross the road?
It wanted to be normal.

Jassim

Guest

Re: prove that

Thanks Ricky and mathsyperson  ... my big mistake was :

if B ^ E = Ø
then B ^ E = B ^ B comlement
E = B complement ! ... thats really stupid

thanks alot !

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: prove that

[Dickinson]\mbox{Assume there is an element }x\in A\cap E.[/Dickinson]