4. Jonathan says, "I will pass the course only if I get 70% or better on the final exam." Jonathan received 65% on the final exam. Can he still pass the course?
5. Sherlock Holmes has discovered that the Baskervilles are innocent, and therefore concluded that their hounds are guilty. Which of the following might have been his hypothesis?
-
The Baskervilles are innocent only if their hounds are guilty.
The hounds are guilty only if the Baskervilles are innocent.
Only the Baskervilles are innocent if their hounds are guilty.
4. Jonathan says, "I will pass the course only if I get 70% or better on the final exam." Jonathan received 65% on the final exam. Can he still pass the course?
You answered:
-
No.
The argument is:
If I pass then I got 70%+ | --or-- |
If P then Q |
5. Sherlock Holmes has discovered that the Baskervilles are innocent, and therefore concluded that their hounds are guilty. Which of the following might have been his hypothesis?
You answered:
-
The Baskervilles are innocent only if their hounds are guilty.
You know one premise and the conclusion here, and so must solve for the missing premise:
- (Missing conditional premise)
- The Baskervilles are innocent
- Their hounds are guilty
- The Baskervilles are innocent
To be valid, the argument must be in one of the valid forms--either modus ponens or modus tollens. In the former, "The Baskervilles are innocent" must be P; in the latter, it must be Not Q. Therefore, the arguments would be as follows:
If Baskervilles are innocent,
The Baskervilles are innocent. Their hounds are guilty. (Affirming the antecedent) | If their hounds are not guilty,
The Baskervilles are innocent. Their hounds are guilty. (Negating the consequent) | |
| --or-- | ||
If P then Q | If P then Q |
Now, the question is only which of the options in question 5 is equivalent to one of the conditional premises above. The answer is the first option: "The Baskervilles are innocent only if their hounds are guilty" is equivalent to "If the Baskervilles are innocent, then their hounds are guilty."
Your answer, "The hounds are guilty only if the Baskervilles are innocent," would be equivalent to a very different conditonal, in which the antecedent and the consequent are reversed: "If the hounds are guilty, then the Baskervilles are innocent."
4. Jonathan says, "I will pass the course only if I get 70% or better on the final exam." Jonathan received 65% on the final exam. Can he still pass the course?
You answered:
-
Yes
The argument is:
If I pass then I got 70%+ | --or-- |
If P then Q |
4. Jonathan says, "I will pass the course only if I get 70% or better on the final exam." Jonathan received 65% on the final exam. Can he still pass the course?
You answered:
-
Unknown.
The argument is:
If I pass then I got 70%+ | --or-- |
If P then Q |
5. Sherlock Holmes has discovered that the Baskervilles are innocent, and therefore concluded that their hounds are guilty. Which of the following might have been his hypothesis?
You answered:
-
The hounds are guilty only if the Baskervilles are innocent.
You know one premise and the conclusion here, and so must solve for the missing premise:
- (Missing conditional
premise)
- The Baskervilles are innocent
- Their hounds are guilty
- The Baskervilles are innocent
To be valid, the argument must be in one of the valid forms--either modus ponens or modus tollens. In the former, "The Baskervilles are innocent" must be P; in the latter, it must be Not Q. Therefore, the arguments would be as follows:
If Baskervilles are innocent,
The Baskervilles are innocent. Their hounds are guilty. (Affirming the antecedent) | If their hounds are not guilty,
The Baskervilles are innocent. Their hounds are guilty. (Negating the consequent) | |
| --or-- | ||
If P then Q | If P then Q |
Now, the question is only which of the options in question 5 is equivalent to one of the conditional premises above.
5. Sherlock Holmes has discovered that the Baskervilles are innocent, and therefore concluded that their hounds are guilty. Which of the following might have been his hypothesis?
You answered:
-
Only the Baskervilles are innocent if their hounds are guilty.
You know one premise and the conclusion here, and so must solve for the missing premise:
- (Missing conditional
premise)
- The Baskervilles are innocent
- Their hounds are guilty
- The Baskervilles are innocent
To be valid, the argument must be in one of the valid forms--either modus ponens or modus tollens. In the former, "The Baskervilles are innocent" must be P; in the latter, it must be Not Q. Therefore, the arguments would be as follows:
If Baskervilles are innocent,
The Baskervilles are innocent. Their hounds are guilty. (Affirming the antecedent) | If their hounds are not guilty,
The Baskervilles are innocent. Their hounds are guilty. (Negating the consequent) | |
| --or-- | ||
If P then Q | If P then Q |
Now, the question is only which of the options in question 5 is equivalent to one of the conditional premises above.
5. Sherlock Holmes has discovered that the Baskervilles are innocent, and therefore concluded that their hounds are guilty. Which of the following might have been his hypothesis?
You answered:
-
The Baskervilles are innocent if their hounds are guilty.
You know one premise and the conclusion here, and so must solve for the missing premise:
- (Missing conditional premise)
- The Baskervilles are innocent
- Their hounds are guilty
- The Baskervilles are innocent
To be valid, the argument must be in one of the valid forms--either modus ponens or modus tollens. In the former, "The Baskervilles are innocent" must be P; in the latter, it must be Not Q. Therefore, the arguments would be as follows:
If Baskervilles are innocent,
The Baskervilles are innocent. Their hounds are guilty. (Affirming the antecedent) | If their hounds are not guilty,
The Baskervilles are innocent. Their hounds are guilty. (Negating the consequent) | |
| --or-- | ||
If P then Q | If P then Q |
Now, the question is only which of the options in question 5 is equivalent to one of the conditional premises above. The answer is the first option: "The Baskervilles are innocent only if their hounds are guilty" is equivalent to "If the Baskervilles are innocent, then their hounds are guilty."
Your answer, "The Baskervilles are innocent if their hounds are guilty," would reverse the order of p and q: "If the hounds are guilty, then the Baskervilles are innocent."
Congratulations! You have finished the exercises for the "Only If Conditionals" section.