1. Demonstrate the validity of the following identities by means of truth tables: (5 pts each) a. DeMorgan’s theorm for three va
riables: (x+y+z)’ = x’y’z’ And (xyz)’ = x’+y’+z’ b. The distributive law: x+yz = (x+y)(x+z)
1 answer:
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.
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Step-by-step explanation:
We have the following statement
A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.
The simple statements from the statement given are:
,
,
, and
This is the truth table.
