1. "P v Q" is best interpreted as (Points : 1)
P or Q but not both P and Q
P or Q or both P and Q
Not both P or Q
P if and only if Q
2. What is the truth value of the sentence "P & ~ P"? (Points : 1)
True
False
Cannot be determined
Not a sentence
3. If P is false, and Q is false, the truth-value of "P ¡êQ" is (Points : 1)
false.
true.
Cannot be determined.
All of the above.
4. The sentence "P ¡ê Q" is best read as
(Points : 1)
If P then Q
If Q then P
P or Q
P if and only if Q
5. The truth table for a valid deductive argument will show (Points : 1)
wherever the premises are true, the conclusion is true.
that the premises are false.
that some premises are true, some premises false.
wherever the premises are true, the conclusion is false.
6. A conditional sentence with a false antecedent is always (Points : 1)
true.
false.
Cannot be determined.
not a sentence.
7. Truth tables can be used to examine (Points : 1)
inductive arguments.
deductive arguments.
abductive arguments.
All of the above
8. In the conditional "P ¡æ Q," "Q is a (Points : 1)
sufficient condition for Q.
sufficient condition for P.
necessary condition for P.
necessary condition for Q.
9. In the truth table for an invalid argument, (Points : 1)
on at least one row, where the premises are all true, the conclusion is true.
on at least one row, where the premises are all true, the conclusion is false.
on all the rows where the premises are all true, the conclusion is true.
on most of the rows, where the premises are all true, the conclusion is true.
10. What is the truth value of the sentence "P v ~ P"? (Points : 1)
True
False
Cannot be determined
Not a sentence
"P v Q" is best interpreted as (Points : 1)
P or Q but not both P and Q
P or Q or both P and Q
Not both P or Q
P if and only if Q
1. "P v Q" is best interpreted as P or Q or both P and Q. This means that the statement is true if either P is true, Q is true, or both P and Q are true. To determine the truth value of "P v Q", you would need to know the truth values of P and Q. If either P or Q is true, or both are true, then "P v Q" is true.
2. The truth value of the sentence "P & ~ P" is False. The symbol "~" represents negation, so "~ P" means "not P". In this case, "P & ~ P" means "P and not P". Since a statement cannot be both true and false at the same time, "P & ~ P" is always false.
3. If P is false and Q is false, the truth-value of "P → Q" (P implies Q) is true. When the antecedent (P) is false, the implication is always true, regardless of the truth value of the consequent (Q). Therefore, in this case, the truth-value of "P → Q" is true.
4. The sentence "P → Q" is best read as "If P then Q". This conditional statement means that if P is true, then Q must also be true. However, if P is false, the truth value of the statement does not depend on the truth value of Q.
5. The truth table for a valid deductive argument will show that wherever the premises are true, the conclusion is true. In a valid deductive argument, the truth of the premises guarantees the truth of the conclusion. Therefore, if all the premises are true, the truth table will show that the conclusion is also true.
6. A conditional sentence with a false antecedent is always true. In a conditional statement "P → Q", if the antecedent (P) is false, the statement is considered vacuously true, regardless of the truth value of the consequent (Q).
7. Truth tables can be used to examine deductive arguments. Deductive arguments rely on logical reasoning and the truth values of statements to determine the validity of an argument. By constructing a truth table, one can analyze the truth values of the premises and determine the truth value of the conclusion, which aids in evaluating the validity of the deductive argument.
8. In the conditional "P → Q," Q is a necessary condition for P. This means that for P to be true, it is necessary for Q to also be true. However, the truth value of P does not affect the truth value of Q.
9. In the truth table for an invalid argument, on at least one row where the premises are all true, the conclusion is false. An invalid argument is one in which the truth of the premises does not guarantee the truth of the conclusion. Therefore, in the truth table for an invalid argument, there will be at least one row where all the premises are true, but the conclusion is false.
10. The truth value of the sentence "P v ~ P" is True. The symbol "~" represents negation, so "~ P" means "not P". In this case, "P v ~ P" means "ot P". Since the statement includes all possibilities by stating ot P, it is always true. This is known as the law of excluded middle.