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MODULE TWO PROBLEM SET
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Jaime Rowland
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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)
(p A q)
.(p V q)
I used a truth table and I found that the last two columns of the table were not equal. So that would make this 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
p->q 9
The truth table I have laid out shows that the last two columns are not equal. So the argument is invalid because (p . q) Aq # p
Ip-q Inverseerror
..q
Per the truth table the values of p are false there fore the argument is invalid
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Part 3. Which of the following arguments are invalid and which are valid? Prove your answer by replacing each proposition with a variable to obtain the form of the argument. Then prove that the form is valid or invalid.
(h)
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.
The patient has high BP (p) or Diabetes (q) or both = p v q The pa-
(q v r) = p v q v r which means the given statement to be not valid.