This is.Boolean Algebrameans+, theORmeans.and theANDmeansx!.X NOT

Use algebraic manipulation to prove that x +yz = (x + y).(x+z)

x + yz = (x+y) AND (x + z) ...

x +yz = xx + xz + xy + xy + yz

= x(x + z + y) + yz

= x + z + y = 1

= x AND 1 = x

x +yz =x + yz

is that correct?

Next problem: prove that (x+y)(x+y!) = x

= xx + xy! + xy + yy!

= x(x + y! + y) + yy!

what does x + y! + y evaluate to? is it 1?

in that case;

=x AND 1 = x

But what does yy! evaluate to?

please help.

I also need to use algebraic manipulation to prove that xy + yz +x!z = xy + x!z using theproperty.consensus

Thank you for your time,

Sham