Which expressions are in conjunctive normal form x y zy z

Which expressions are in conjunctive normal form?

(x + y + z)(y + z)

z (x + w) *the z has a bar over it

(xyz)(x+z)

(z + y) (x + y) *a long bar over x+y

Solution

The Conjuctive Natural Form (CNF) is the boolean logic represented as AND of OR

i.e. (X+Y) AND (Z) is conjecture but (XY) V Z is not in conjecture natural form

a) (x+y+z)(y+z)

This is in conjecture natural form since it is the AND of two OR\'s i.e. (x,y,z) and (y,z)

b) z\'(x+w)

This is in conjecture natural form since it is the AND of two OR\'s i.e. (x,y,z) and (y,z)

c) (xyz)(x+z)

This is not in conjecture natural form since first term contains AND not OR\'s, hence it is not in CNF form

d) (z+y)\'(x+y)

=> (z\'.y\')(x+y)

This is not in conjecture natural form since first term contains AND not OR\'s, hence it is not in CNF form

The last term is not clear please post it clearly. Thanks