1. Construct the truth table for the compound proposition: [p
(q r)] (r p)
p q r
-------------------------------------------------------------
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
2. What is the negation of the quantified statement:
For every integer, x, there is an integer, y, such that x + y = 0.
3. Use the rules of inference to deduce the following conclusion from
the following set of premises.
Premises: p r
r q
p s t
~q
~r u s
Conclusion: t
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following is a Valid Argument and justify your
reasoning:
All movie stars drive fast cars.
Dan Gordon drives a fast car.
Therefore, Dan Gordon is a movie star.
5. Later in this course, we will study the Inclusion-Exclusion Rule:
|A B C| = |A| + |B| + |C| |A B| |A
C| |B C| + |A B C|.
Verify this for the sets A = {2,3,7,9}, B = {2,3,4}, and C =
{1,3,5,7,9}.
6. Find A B for the sets A = { , {} } and B = { {}, {0} }
Mathematics Homework Solutions
#8207
Discrete Math: Logic Problems, Truth Table and Rules of Inference
Please see the attached file for the fully formatted problems.
1. Construct the truth table for the compound proposition: [p (q r)] (r p)
p q r
-------------------------------------------------------------
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
2. What is the negation of the quantified statement:
For every integer, x, there is an integer, y, such that x + y = 0.
3. Use the rules of inference to deduce the following conclusion from the following set of premises.
Premises: p r
r q
p s t
~q
~r u s
Conclusion: t
4. Decide if the following is a Valid Argument and justify your reasoning:
All movie stars drive fast cars.
Dan Gordon drives a fast car.
Therefore, Dan Gordon is a movie star.
5. Later in this course, we will study the Inclusion-Exclusion Rule:
|A B C| = |A| + |B| + |C| |A B| |A C| |B C| + |A B C|.
Verify this for the sets A = {2,3,7,9}, B = {2,3,4}, and C = {1,3,5,7,9}.
6. Find A B for the sets A = { , {} } and B = { {}, {0} }
Logic problems are solved. The solution is detailed and well presented.
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