1) In the truth table for an invalid argument,
Student Answer: on at least one row, where the premises are all true, the conclusion is true.
CORRECT 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.
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
2. Question : The truth table for a valid deductive argument will show
Student Answer: CORRECT wherever the premises are true, the conclusion is true.
that the premises are false.
INCORRECT that some premises are true, some premises false.
wherever the premises are true, the conclusion is false.
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
3. Question : Truth tables can be used to examine
Student Answer: INCORRECT inductive arguments.
CORRECT deductive arguments.
abductive arguments.
All of the above
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
4. Question : A conditional sentence with a false antecedent is always
Student Answer: CORRECT true.
false.
Cannot be determined.
not a sentence.
Instructor Explanation: The answer can be found in Chapter Six of An Introduction to Logic.
5. Question : Truth tables can determine which of the following?
Student Answer: CORRECT If an argument is valid
If an argument is sound
If a sentence is valid
All of the above
6. Question : "P v Q" is best interpreted as
Student Answer: P or Q but not both P and Q
CORRECT P or Q or both P and Q
Not both P or Q
P if and only if Q
7. Question : What is the truth value of the sentence "P v ~ P"?
Student Answer: CORRECT True
INCORRECT False
Cannot be determined
Not a sentence
8. Question : One of the disadvantages of using truth tables is
Student Answer: INCORRECT it is difficult to keep the lines straight
T's are easy to confuse with F's.
CORRECT they grow exponentially and become too large for complex arguments.
they cannot distinguish strong inductive arguments from weak inductive arguments.
9. Question : "Julie and Kurt got married and had a baby" is best symbolized as
Student Answer: M v B
CORRECT M & B
M ¡æ B
M ¡ê B
10. Question : If P is false, and Q is false, the truth-value of "P ¡êQ" is
Student Answer: false.
CORRECT true.
Cannot be determined.
All of the above.
What is this? An exam??
1) In the truth table for an invalid argument, on at least one row, where the premises are all true, the conclusion is false.
2) The truth table for a valid deductive argument will show wherever the premises are true, the conclusion is true.
3) Truth tables can be used to examine deductive arguments.
4) A conditional sentence with a false antecedent is always true.
5) Truth tables can determine if an argument is valid.
6) "P v Q" is best interpreted as P or Q or both P and Q.
7) The truth value of the sentence "P v ~ P" is true.
8) One of the disadvantages of using truth tables is that they grow exponentially and become too large for complex arguments.
9) "Julie and Kurt got married and had a baby" is best symbolized as M & B.
10) If P is false and Q is false, the truth-value of "P → Q" is true.
1) The correct answer is "on at least one row, where the premises are all true, the conclusion is false." To determine this, you need to create a truth table for the argument in question. In the truth table, you would list all possible combinations of truth values for the premises and the conclusion, and then evaluate the conclusion based on the truth values of the premises. If there is at least one row where the premises are all true and the conclusion is false, then the argument is invalid.
2) The correct answer is "wherever the premises are true, the conclusion is true." To determine this, you again need to create a truth table for the argument. If in every row where the premises are all true, the conclusion is also true, then the argument is valid.
3) The correct answer is "deductive arguments." To determine this, you need to understand the difference between deductive and inductive reasoning. Deductive arguments are characterized by the fact that if the premises are true, then the conclusion must be true. Inductive arguments, on the other hand, are characterized by the fact that the premises make the conclusion more likely, but do not guarantee its truth. Truth tables are used to examine the validity of deductive arguments.
4) The correct answer is "false." To determine this, you need to understand the truth conditions of conditional sentences. A conditional sentence of the form "if P, then Q" is only false if the antecedent (P) is true and the consequent (Q) is false. If the antecedent is false, the whole conditional sentence is always true, regardless of the truth value of the consequent.
5) The correct answer is "If an argument is valid." Truth tables can determine the validity of arguments by evaluating all possible truth value combinations for the premises and the conclusion. If in every row where the premises are all true, the conclusion is also true, then the argument is valid.
6) The correct answer is "P or Q or both P and Q." The expression "P v Q" represents the logical disjunction, which is true if either P is true, or Q is true, or both P and Q are true.
7) The correct answer is "True." The sentence "P v ~ P" represents a logical tautology, meaning it is always true regardless of the truth value of P. This is because the disjunction between P and its negation (~ P) will always be true, since at least one of them must be true.
8) The correct answer is "they grow exponentially and become too large for complex arguments." Truth tables become larger as the number of variables in the argument increases. For complex arguments with many variables, the truth table can become extremely large and difficult to manage.
9) The correct answer is "M & B." The sentence "Julie and Kurt got married and had a baby" can be symbolized using the conjunction operator "&" to represent the logical "and" between the propositions M (Julie got married) and B (Julie and Kurt had a baby).
10) The correct answer is "true." To determine this, you need to evaluate the truth value of the conditional sentence "P -> Q" based on the truth values of P and Q. If the antecedent (P) is false, the conditional sentence is always true, regardless of the truth value of the consequent (Q).