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MODULE TWO PROBLEM SET
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Beth Campbell
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Directions: Type your solutions into this document and be sure to show all steps for arriving at your solution. Just giving a final number may not receive full credit.
PROBLEM 1
Part 1. Indicate whether the argument is valid or invalid. For valid arguments, prove that the argument is valid using a truth table. For invalid arguments, give truth values for the variables showing that the argument is not valid.
(1)
l(bVa)
..(p V q) r
After creating a truth table, the last two columns are not equal. Therefore, the argument is invalid.
Part 2. Converse and inverse errors are typical forms of invalid argu- ments. Prove that each argument is invalid by giving truth values for the variables showing that the argument is invalid. You may find it eas- ier to find the truth values by constructing a truth table.
(a) Converse error
b
..p
In hypothesis part 1: P can be falst but q must be true for the argument to be valid.
In hypothesis part 2: q is true.
Conclusion: P can be true or false.
After constructing a truth table, there is an error between the 2nd part of the hypothesis
and the conclusion. Therefore, the argument is invalid.
snhu
(b) Inverse error
p
p
After constructing a truth table, the third row is a critical row,
and the conclusion in that row is false.
Therefore, the argument is invalid.
Part 3. Which of the following arguments are invalid and which are
to obtain the form of the argument. Then prove that the form is valid or invalid.
(a)
The patient has high blood pressure or diabetes or both. The patient has diabetes or high cholesterol or both
.. The patient has high blood pressure or high cholesterol
let p represent high blood pressure
let q represent diabetes
let r represent high cholesterol.
p Vq
q V r
.. pV r
If p and r are false
and q is true then both pVq and qVr
are true but pVr is false