Question

1. Demonstrate the validity of the following identities by means of truth tables: (5 pts each) a. DeMorgan’s theorm for three variables: (x+y+z)’ = x’y’z’ And (xyz)’ = x’+y’+z’ b. The distributive law: x+yz = (x+y)(x+z)

Answer 1

Answer:

All the three statements presented are indeed valid and satisfy the De Morgan's theorem.

Step-by-step explanation:

The truth tables are presented in the attached images.

a) The statement (X + Y + Z)' = (X'Y'Z') has its proof in the first image attached.

b) The statement (XYZ)' = (X' + Y' + Z') has its proof in the second image attached.

c) The statement (X + YZ) = (X + Y)(X + Z) has its proof in the third image attached.