1. A conditional sentence with a false antecedent is always (Points : 1)
true.
false.
Cannot be determined.
not a sentence.
2. "Julie and Kurt got married and had a baby" is best symbolized as (Points : 1)
M v B
M & B
M → B
M ↔ B
3. Truth tables can determine which of the following? (Points : 1)
If an argument is valid
If an argument is sound
If a sentence is valid
All of the above
4. Truth tables can be used to examine (Points : 1)
inductive arguments.
deductive arguments.
abductive arguments.
All of the above
5. 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.
6. If P is true, and Q is false, the truth-value of "P v Q" is (Points : 1)
false.
true.
Cannot be determined
All of the above
7. 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.
8. What is the truth value of the sentence "P v ~ P"? (Points : 1)
True
False
Cannot be determined
Not a sentence
9. "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
10. In the conditional "P →Q," "P" is a (Points : 1)
sufficient condition for Q.
sufficient condition for P.
necessary condition for P.
necessary condition for Q.
Truth tables can
1. To determine the answer to this question, we need to understand what a conditional sentence with a false antecedent means. A conditional sentence has the form "If A, then B," where A is the antecedent and B is the consequent. In this case, we are given that the antecedent is false. According to the truth table for conditionals, when the antecedent is false, the conditional is always true. Therefore, the correct answer is true.
2. To symbolize the statement "Julie and Kurt got married and had a baby," we need to understand how to represent "and" in logic. The correct symbol for "and" is "&". Therefore, the best symbolization for the statement is M & B.
3. Truth tables can determine if an argument is valid, if an argument is sound, and if a sentence is valid. Validity refers to the logical structure of an argument, while soundness refers to both the logical structure and the truth of the premises. Therefore, the correct answer is "All of the above."
4. Truth tables can be used to examine deductive arguments. Deductive arguments are those in which the conclusion follows necessarily from the premises, and truth tables are a useful tool to determine the logical validity of such arguments. Therefore, the correct answer is deductive arguments.
5. In the truth table for an invalid argument, there will be at least one row where the premises are all true, but the conclusion is false. Valid arguments, on the other hand, have all true premises leading to a true conclusion. Therefore, the correct answer is "on at least one row, where the premises are all true, the conclusion is false."
6. To find the truth value of "P v Q," we need to know the truth values of P and Q. If P is true and Q is false, the truth value of "P v Q" is true. The "v" symbol represents the logical OR, and in this case, when at least one of the statements is true, the entire statement is true. Therefore, the correct answer is true.
7. The truth table for a valid deductive argument will show that wherever the premises are true, the conclusion is true. This is because a valid argument follows the rules of deductive logic, where the truth of the premises guarantees the truth of the conclusion. Therefore, the correct answer is "wherever the premises are true, the conclusion is true."
8. The truth value of the sentence "P v ~ P" can be determined using the truth value of P. The symbol "~" represents negation, so "~ P" means "not P." In this case, "P v ~ P" means "ot P." In logic, the principle of "Law of Excluded Middle" states that a statement is either true or false, but not both. Therefore, the truth value of "P v ~ P" is true. Therefore, the correct answer is true.
9. "P v Q" is best interpreted as P or Q or both P and Q. The symbol "v" represents the logical OR, which means that at least one of the statements P or Q needs to be true for the entire statement to be true. Therefore, the correct answer is P or Q or both P and Q.
10. In the conditional "P → Q," "P" is a necessary condition for Q. In a conditional statement, the antecedent (P) is the necessary condition, while the consequent (Q) is the sufficient condition. This means that if P is true, then it is necessary for Q to be true as well. However, if P is false, the truth value of Q is independent. Therefore, the correct answer is necessary condition for Q.