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)

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.

step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it