Question

solve X' ((Y.Z)' + Y'​

Answer 1

Explanation:

2-1: Demonstrate by means of truthtables

Points to remember:

1. truth tables ARE proof

2. proof by truthtable is time intensive -- it is better to simplify

first.

3. group, then analyze (make it as mechanical as possible)

(a) Demorgan's Theorem for three variables: (XYZ)' = X' + Y' + Z'

X Y Z XYZ (XYZ)' X'+Y'+Z'

0 0 0 0 1 1

0 0 1 0 1 1

0 1 0 0 1 1

0 1 1 0 1 1

1 0 0 0 1 1

1 0 1 0 1 1

1 1 0 0 1 1

1 1 1 1 0 0

Observe that the general form (the negation of some expression

ABCDEF...XYZ) will follow the same pattern. Why?

(b) X + YZ = (X+Y)(X+Z)

(algebraic solution: XX+XY+XZ+YZ = X(1+Y+Z)+YZ = X+YZ)

(speed tip: note that in + sets you should scan & fill in the leftmost

variable first, marking as true, then the rightmost (alternating), and

so on -- e.g., in X+YZ below you can fill in the bottom four 1's

automatically)