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

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- October 3rd 2011, 08:46 PMJskidhow are these two statments logically equivalent?
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It's not apparent how these are logically equivalent, could someone please elaborate? - October 3rd 2011, 09:00 PMissacnewtonRe: how are these two statments logically equivalent?
the second statement should be written as

this follows from the first statement using distributive law

Boolean algebra (logic) - Wikipedia, the free encyclopedia - October 3rd 2011, 09:23 PMJskidRe: how are these two statments logically equivalent?
But wouldn't that distribute as which isn't the same as the prior step

- October 3rd 2011, 10:22 PMissacnewtonRe: how are these two statments logically equivalent?
yes you are right. you have further used the distributive law.

further you can see that

are tautologies. so we can further simplify as

- October 3rd 2011, 10:44 PMJskidRe: how are these two statments logically equivalent?
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)

- October 3rd 2011, 10:49 PMissacnewtonRe: how are these two statments logically equivalent?
do you understand now ?