Intersection and Union of Sets

[samistumbo]

Okay, I have the following problem: Show that (A n B) u C and A n (B u C) need not be equal sets.

Is the question asking, or saying, that (A n B) u C does not equal A n (B u C), but it wants me to show why?

I can visualize this with the 3 ring venn diagram and explain it in words, but how do I show what I know mathematically?

I think I'm right in assuming they're not equal because (A n B) u C will include everything because it has a union with C, while A n (B u C) will only contain what intersects with A.

 

[pka]

Okay, I have the following problem: Show that (A n B) u C and A n (B u C) need not be equal sets.

Let \(\displaystyle A=\{1,2\},~B=\{2,3\}~\&~C=\{1,3\}\).

 

[samistumbo]

Let \(\displaystyle A=\{1,2\},~B=\{2,3\}~\&~C=\{1,3\}\).

So, (A n B) u C= {1, 2, 3} and A n (B u C)= {1, 3}

{1, 2, 3} does not equal {1, 3}
?