I need to prove A intersect (B U C)=(A intersect B)U(A intersect C).

I'm having trouble getting started....

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- November 4th 2008, 06:33 AMkathrynmathA intersect (B U C)
I need to prove A intersect (B U C)=(A intersect B)U(A intersect C).

I'm having trouble getting started.... - November 4th 2008, 07:30 AMJhevon
- November 4th 2008, 07:37 AMpoutsos.B
- November 4th 2008, 09:44 AMkathrynmath
So, can I let x be an element of Ahttp://www.mathhelpforum.com/math-he...c7f8f01c-1.gif(BUC). So x is an elemnt of A and B or C?

- November 5th 2008, 07:04 PMJhevon
- November 7th 2008, 02:21 AMpoutsos.B

Let xεA mean x is an element of A e.t.c,et.c.

Now xe[Α ( BUC)] is equivalent to xεΑ and (xεB or xεC) due to the definition of intersection and union of sets.

This is now the crucial point of the problem.Usually here a lot of people get stuck.Only those with a good knowledge of propositional logic have no problem.

So put now :.........xεΑ =p,................xεB=q,................xεC=r,... .........and xεΑ and (xεB or xεC) becomes p^(qvr)........................................... .....................1

(1) is now a statement in propositional logic where p,q,r can be any true or false proposition:

So put :......p= i go to town ,.........q= i go to the movies,...........................r= i go to the theater and (1) becomes :

i go to town and i go to the movies or to the theater:

Now ask your logic what this is equivalent with??????????

Once you come with an answer convert your answer into letters p,q,r using the above transformation.

Finally put now p=xεA ....e.t.c,e.t.c.

What is the result now?????