Hello all,(adsbygoogle = window.adsbygoogle || []).push({});

I'm having a hard time trying to prove a few things. I'm looking for a little help because I cannot seem to grasp the concept of proofs and what constitutes a valid proof and if my proof is wrong, correcting it.

I have a proof done and if anyone could "critique" it I would be very grateful.

Prove: (A [tex]\cup[/tex] B) X C = (A X C) [tex]\cup[/tex] (B X C)

Proof:

Let x [tex]\in[/tex] (A [tex]\cup[/tex] B) X C

Then x is of the type (y,z) where y [tex]\in[/tex] A and z [tex]\in[/tex] C

Then y [tex]\in[/tex] A or y [tex]\in[/tex] B

Since z [tex]\in[/tex] C, (y,z) [tex]\in[/tex] A X C or

Since z [tex]\in[/tex] C, (y,z) [tex]\in[/tex] B X C

Then (y,z) [tex]\in[/tex] (A X C) [tex]\cup[/tex] (B X C)

Therefore (A [tex]\cup[/tex] B) X C = (A X C) [tex]\cup[/tex] (B X C)

Thanks for your time,

Ryan

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# Proofs on sets help

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