Question

The Boolean expression wxyz+u+v is equivalent to an expression in 3-CNF (a product of clauses, each clause being the sum of exactly three literals). Find the simplest such 3-CNF expression and then identify one of its clauses in the list below. Note: -e denotes the negation of e. Also note: we are looking for an expression that involves only u, v, w, x, y, and z, no other variables. Not all boolean expressions can be converted to 3-CNF without introducing new variables, but this one can.(a) (w+z+u)

(b) (y+z+v)
(c) (x+y+v)
(d) (z+u+v)

Answer 1

Option d: (z+u+v)

is the correct answer.

Step-by-step explanation:

Given Boolean expression:

B=w.x.y.z+u+v

By applying brackets:

B=w.x.y.z+(u+v) ......... eq(1)

Now we will apply the AND Distributive law that says:

( A + (B.C) = (A + B).(A + C)

So the equation 1 will become:

B=(w+u+v).(x+u+v).(z+u+v)

Hence this is the 3-CNF form

So the answer is (z+u+v), as it as a literal in 3-CNF

i hope it will help you!