a) Using long or short truth tables (symbolize as necessary and show tables) determine and state whether the following arguments are valid, briefly explaining your table; and b) if valid, demonstrate validity by deductions using Group I rules.
Arg
1. P-->Q
2. ~P ^:~Q
Arg
If Peter is perceptive, then Quincy is a quack. Quincy, however, is not a quack. So Peter's not perceptive. (Hint: this is a valid argument)
This logical argument is valid under the following condition.
If and only if Peter is perceptive, then Quincy is a quack. Quincy, however, is not a quack. So Peter's not perceptive.
Truth table
PP QQ
T T
F F
I have no idea what you mean by group I rules.
To determine the validity of the argument, we can construct a truth table.
1. Let P represent "Peter is perceptive."
2. Let Q represent "Quincy is a quack."
1. P --> Q can be represented as ~P V Q.
2. ~P ^ ~Q can be represented as ~(P V Q).
Now, construct a truth table with the columns for P, Q, P --> Q, and ~(P V Q).
P | Q | P --> Q | ~(P V Q)
---------------------------
T | T | T | F
T | F | F | F
F | T | T | F
F | F | T | T
In the first row, both P and Q are true. According to the conditional statement P --> Q, the result is true. However, ~(P V Q) is false. This means that the argument is not valid because it does not hold true for all possible truth value combinations.
The requested Group I rules refer to a specific set of inference rules, but they are not mentioned in the problem statement. Therefore, without further information about Group I rules, it is not possible to demonstrate validity using them.