I really need some help on these questions Please! I am having a very tough time. I have tried to answer to the best of my ability, but i am not understanding these. Can someone please help with this? Thank you.
Truth tables can be used to examine inductive arguments.
deductive arguments.
abductive arguments.
All of the above
my answer d
2. Truth tables can
display all the possible truth values involved with a set of sentences.
determine what scientific claims are true.
determine if inductive arguments are strong.
determine if inductive arguments are weak.
my answer a
3. What is the truth value of the sentence "P & ~ P"?
True
False
Cannot be determined
Not a sentence
my answer c
4. In the truth table for an invalid argument,
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.
my answer b
5. If P is false, and Q is false, the truth-value of "P ¡êQ" is
false.
true.
Cannot be determined.
All of the above.
my answer a
6. The sentence "P ¡ê Q" is best read as
If P then Q
If Q then P
P or Q
P if and only if Q
my answer d
7. "~ P v Q" is best read as Not P and Q
It is not the case that P and it is not the case that Q
It is not the case that P or Q
It is not the case that P and Q
my answer c
8. A sentence is said to be truth-functional if and only if
the sentence might be true.
the truth-value of the sentence cannot be determined from the truth values of its components.
the truth-value of the sentence is determined always to be false.
the truth-value of the sentence can be determined from the truth values of its components.
my answer d
9. The sentence "P ¡æ Q" is read as
P or Q
P and Q
If P then Q
Q if and only P
my answer c
10. In the conditional "P ¡æQ," "P" is a
sufficient condition for Q.
sufficient condition for P.
necessary condition for P.
necessary condition for Q.
my answer b
Please let me know if these are correct.
1. Truth tables can be used to examine:
Correct answer: (a) inductive arguments.
To determine the correct choice, let's break it down:
- Deductive arguments are based on logical reasoning and the truth values of their premises guarantee the truth value of the conclusion. Truth tables are not typically used for evaluating deductive arguments.
- Abductive arguments are concerned with reasoning and inference to the best explanation. Truth tables are not commonly used in evaluating abductive arguments.
- Inductive arguments, on the other hand, involve reasoning from specific observations to general conclusions. Truth tables can be used to examine the truth values of the premises and conclusion in inductive arguments. Therefore, the correct answer is (a) inductive arguments.
2. Truth tables can:
Correct answer: (a) display all the possible truth values involved with a set of sentences.
To determine the correct choice, let's break it down:
- Truth tables are primarily used to display all the possible combinations of truth values for a set of sentences or propositions. This helps in determining the truth value of compound statements based on the truth values of the individual propositions involved.
- While truth tables can indirectly help in assessing the validity of inductive arguments, it is not their primary purpose. Determining the truth value of scientific claims or evaluating the strength of inductive arguments is beyond the scope of truth tables.
Based on this analysis, the correct answer is (a) display all the possible truth values involved with a set of sentences.
3. What is the truth value of the sentence "P & ~ P"?
Correct answer: (b) False.
To determine the correct choice, let's break it down:
- "P & ~ P" represents the conjunction (AND) between proposition P and the negation of proposition P (represented as ~P).
- The truth table for the conjunction operator states that P & Q is true only when both P and Q are true.
- In the case of "P & ~ P," if P is true, then ~P is false, resulting in a false conjunction. If P is false, then ~P is true, again resulting in a false conjunction.
- Since the conjunction is false for all possible truth values of P, the correct answer is (b) False.
4. In the truth table for an invalid argument,...
Correct answer: (a) on at least one row, where the premises are all true, the conclusion is true.
To determine the correct choice, let's break it down:
- In a truth table for an argument, the rows represent different combinations of truth values for the premises and conclusion.
- An invalid argument is one where there exists at least one row in the truth table where the premises are all true, but the conclusion is false. This indicates that the argument does not have a valid deduction.
- Therefore, the correct answer is (a) on at least one row, where the premises are all true, the conclusion is true.
5. If P is false, and Q is false, the truth-value of "P ¡êQ" is...
Correct answer: (a) false.
To determine the correct choice, let's break it down:
- "P ¡êQ" represents the conditional statement, "if P, then Q."
- In a conditional statement, if the antecedent (P) is false, then the overall conditional statement is always true, regardless of the truth value of the consequent (Q).
- Therefore, if P is false, the correct answer is (a) false.
6. The sentence "P ¡ê Q" is best read as...
Correct answer: (a) If P then Q.
To determine the correct choice, let's break it down:
- "P ¡ê Q" represents a conditional statement.
- The phrase "If P then Q" captures the essence of the conditional relationship. It indicates that if P is true, it implies that Q must also be true.
- Therefore, the correct answer is (a) If P then Q.
7. "~ P v Q" is best read as...
Correct answer: (c) It is not the case that P or Q.
To determine the correct choice, let's break it down:
- "~ P" represents the negation of proposition P. It is read as "not P."
- "v" represents the logical operator for disjunction (OR).
- Therefore, "~ P v Q" is best read as "It is not the case that P or Q."
8. A sentence is said to be truth-functional if and only if...
Correct answer: (d) the truth-value of the sentence can be determined from the truth values of its components.
To determine the correct choice, let's break it down:
- Truth-functional sentences are those where the truth value of the entire sentence can be determined solely based on the truth values of its individual components (propositions or sentences).
- The other choices do not accurately describe truth-functional sentences. For example, a truth-functional sentence can have a truth value that is always true or always false.
- Therefore, the correct answer is (d) the truth-value of the sentence can be determined from the truth values of its components.
9. The sentence "P ¡æ Q" is read as...
Correct answer: (c) If P then Q.
To determine the correct choice, let's break it down:
- "P ¡æ Q" represents the material conditional (implication) between proposition P and proposition Q.
- The phrase "If P then Q" accurately captures the meaning of the material conditional.
- Therefore, the correct answer is (c) If P then Q.
10. In the conditional "P ¡æQ," "P" is a...
Correct answer: (c) necessary condition for P.
To determine the correct choice, let's break it down:
- In a conditional statement "P ¡æQ", P represents the antecedent (the condition), and Q represents the consequent.
- A necessary condition is something that must be true for the consequent to be true. In this case, P is necessary for Q to be true.
- Therefore, the correct answer is (c) necessary condition for P.
Based on the explanations provided, please review your answers and make any necessary corrections.