1) Construct the Truth Table for each of the following Boolean expressions:
Are they equivalent expressions? Are they tautologies? Contradictions?
2) Find a Boolean expression involving x y which produces the following table:
3) Consider a statement of the form "if A then (B and C)". Assume you wish to disprove it. Then you need to provide a counterexample, that is, you need to exhibit an instance for which
a) B and C are false
b) A is true and both B and C are false
c) B is false or C is false
d) A is true and B is false, or A is true and C is false
e) A is false, B is false, and C is false
Indicate which of the above is the correct answer.© BrainMass Inc. brainmass.com October 10, 2019, 5:15 am ad1c9bdddf
Please see the attached files.
We use the equivalency:
And two De-Morgan rules:
The truth tables for the basic operations:
F F F F
F T T F
T F T F
T T T T
The first expression can be converted using De-Morgan rule (b):
The truth table is:
F F T F
F T F F
T F T T
T T F F
The expression is simplified:
This is a simple OR operation, so the truth table is:
F F F
F T T
T F T
T T T
The expression can be simplifies using De-Morgan rule (a):
This is a simple NAND operator. It ...
The expert examines truth tables in discrete mathematics. Counterexamples are provided.