Discrete Math: Truth Tables
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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.
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Solution Summary
The expert examines truth tables in discrete mathematics. Counterexamples are provided.
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We use the equivalency:
(1.1)
And two De-Morgan rules:
(1.2)
The truth tables for the basic operations:
F F F F
F T T F
T F T F
T T T T
1.
The first expression can be converted using De-Morgan rule (b):
(1.3)
The truth table is:
F F T F
F T F F
T F T T
T T F F
2.
The expression is simplified:
(1.4)
This is a simple OR operation, so the truth table is:
F F F
F T T
T F T
T T T
3.
The expression can be simplifies using De-Morgan rule (a):
(1.5)
This is a simple NAND operator. It ...
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