Using DeMorgan's Law, write an expression for the complement of F if F(x,y,z)= xy + x'z + yz'
I know this property:
(x'y') = (x' + y') and (x' + y') = x'y'
But there's only one variable that is NOT'ed at a time, (x in the x'z and y in yz').
Using DeMorgan's Law, write an expression for the complement of F if F(x,y,z)= xy + x'z + yz'
I know this property:
(x'y') = (x' + y') and (x' + y') = x'y'
But there's only one variable that is NOT'ed at a time, (x in the x'z and y in yz').
No, it's (xy)' = (x' + y') and (x + y)' = x'y'. The left-hand side is the negation of a conjunction or a disjunction.
You don't need to transform F(x,y,z); you need to transform its negation. F is a sum (disjunction), so it's negation can be rewritten by De Morgan's law.
To begin with, emakarov solved the problem.
I was curious about what it was about, so,
P^Q: (and), PvQ: (or) have truth table definitions for P,Q True or False.
T’=F and F’ =T by definition.
From the truth table definitions:
(P^Q)’=P’vQ'
(PvQ)’=P’^Q’
By definition, in this context, • is ^ and + is v
Reference wiki “DeMorgans Laws”