how are these two statments logically equivalent?

http://img855.imageshack.us/img855/5706/helpjw.png

It's not apparent how these are logically equivalent, could someone please elaborate?

the second statement should be written as



this follows from the first statement using distributive law

Boolean algebra (logic) - Wikipedia, the free encyclopedia

But wouldn't that distribute as which isn't the same as the prior step

yes you are right. you have further used the distributive law.
further you can see that


are tautologies. so we can further simplify as

I couldn't see that b/c I was trying to think of how to apply the distributive law differently. I never occured to me that I needed to do another step (i.e. remove tautologies)

do you understand now ?