From these premises...
Ken is a killer and Sam is a saint.
Ken is a killer.
...which of the following conclusions are implied?
a. Sam is a saint.
b. Ken is a killer or Sam is a saint.
c. Sam is a saint or Sam is not a saint.
d. All of the above are implied
e. None of the above are implied.
I am sure that a and c are implied, but am not sure if b is (which would make the correct answer d, all of the above). I am leaning toward just a and c...
Thanks!
The only one that is stated is "Sam is a saint". There is no "or" in the premises
To determine which conclusions are implied from the given premises, we need to analyze the logical connections between the statements.
The first premise states: Ken is a killer and Sam is a saint.
The second premise states: Ken is a killer.
Based on the first premise, we can infer that Sam is a saint because it is explicitly mentioned.
Regarding the second premise, it does not provide any new information as it only repeats what was already mentioned in the first premise. Therefore, we cannot draw any new conclusions from it.
Now let's evaluate each conclusion:
a. Sam is a saint. - This conclusion is directly implied from the first premise, so it is correct.
b. Ken is a killer or Sam is a saint. - This conclusion is a combination of the information provided in the premises. The first premise states that Ken is a killer, and the same premise states that Sam is a saint. Since either Ken is a killer or Sam is a saint, this conclusion is also correct.
c. Sam is a saint or Sam is not a saint. - This conclusion is not logical based on the given premises. The premises do not provide any information or contradiction about whether Sam is not a saint. Therefore, we cannot infer this conclusion.
d. All of the above are implied. - Since conclusion c is not logical based on the premises, the correct answer cannot be d.
e. None of the above are implied. - Conclusion a is implied, and conclusion b is also implied, so this choice is incorrect.
Based on the analysis, the correct answer is b. Ken is a killer or Sam is a saint.