# Can Anyone Figure Out This Problem(Greatly Appreciated!!)

• February 21st 2010, 04:38 PM
rkn0720
Can Anyone Figure Out This Problem(Greatly Appreciated!!)
This is Boolean Algebra. I have to prove that these two sides are equivalent without using a truth table(I already did that.).

(x'^y'^z)v(x^y'^z)v(x^y^z)=(x^z)v(y'^z)

I am using (^) as "and" and (v) as "or"

• February 21st 2010, 04:40 PM
rkn0720
By the way, I have to make the left side equivalent to the right side...
• February 21st 2010, 06:59 PM
simulacrum
Distributivity
Quote:

Originally Posted by rkn0720
This is Boolean Algebra. I have to prove that these two sides are equivalent without using a truth table(I already did that.).

(x'^y'^z)v(x^y'^z)v(x^y^z)=(x^z)v(y'^z)

I am using (^) as "and" and (v) as "or"

There may be a shorter way, but I would use the distributive property. I.e., $a \lor (b \land c) = (a \lor b) \land (a \lor c)$.