#15 - Most cats like to go outside to play when the temperature is above freezing.

[Luke Haqq]

Complete Question Explanation

Must Be True. The correct answer choice is (E).

We can break this down into a handful of conditional statements.

"Jamil does not allow his cat to go outside unless at least one member of his family is outside"

CO FO

In other words, if the cat is outdoors, then a family member is outdoors.

"Jamil's family members go outside only when the sun is shining or it is hot outside"

FO SS OR H

If a family member is outdoors, then the sun must be out or it must be hot.

We can combine these conditional statements into a chain:

CO FO SS OR H

From this, we can infer:

CO SS OR H

That is, if the cat is outdoors, then the sun must be shining or it must be hot. We can also reflect the same information using the contrapositive:

SS AND H CO

If the sun is not shining and it is not hot out, then the cat must not be outdoors.


Answer choice (A): We only know that "most" cats like to go out to play when it is above freezing. This doesn't mean that most like to go out only when it is above freezing. It's possible that Jamil's cat likes to go outside even when it's not above freezing.

Answer choice (B): We know what must be true if the cat is outside--it must be sunny or hot out. But we don't know what must be true if the cat is inside--it might be sunny and hot, or could be cloudy and hot, or cloudy and cold, or sunny and cold. Or it could be nighttime. In short, we don't know what must be true of the weather conditions if the cat is not outdoors.

Answer choice (C): We know that the sun shining or it being hot is a necessary condition for the cat to be outdoors (since one of those conditions is necessary for a family member to be outdoors). This isn't sufficient, however, to guarantee that the cat will be outdoors. In addition, this answer choice uses the word "probably," and we don't have a statement in the stimulus indicating that most cats go outside when it is sunny or hot out.

Answer choice (D): This is a Mistaken Reversal. We know that if the cat is outside, then a family member is outside. Just because a family member is outside, however, doesn't mean that the cat must also be outside.

Answer choice (E): This is the correct answer choice. This answer is reflected in the final conditional statement, the contrapositive of the chained statements.

[AubreyMueller]

I only wanted to check if my logic was correct:

1# Original premise (Unless):

Cat Outside at least one family member outside

Contra positive:
̶a̶t̶ ̶l̶e̶a̶s̶t̶ ̶o̶n̶e̶ ̶f̶a̶m̶i̶l̶y̶ ̶m̶e̶m̶b̶e̶r̶ ̶o̶u̶t̶s̶i̶d̶e̶ ̶C̶a̶t̶ ̶O̶u̶t̶s̶i̶d̶e̶

2# Original premise: (Member outside ONLY IF sun shining OR hot outside)

member outside sun shining OR hot outside

Contra positive:

̶s̶u̶n̶ ̶s̶h̶i̶n̶i̶n̶g̶ ̶ AND ̶ ̶h̶o̶t̶ ̶o̶u̶t̶s̶i̶d̶e̶ ̶m̶e̶m̶b̶e̶r̶ ̶o̶u̶t̶s̶i̶d̶e̶ ̶ ̶

Infrence (correct answer: both premises are taken together):

̶s̶u̶n̶ ̶s̶h̶i̶n̶i̶n̶g̶ ̶ AND ̶ ̶h̶o̶t̶ ̶o̶u̶t̶s̶i̶d̶e̶ ̶m̶e̶m̶b̶e̶r̶ ̶o̶u̶t̶s̶i̶d̶e̶ ̶ ̶ ̶C̶a̶t̶ ̶O̶u̶t̶s̶i̶d̶e̶ = (E)

This is what I did to get the answer for this question, but I fear something in my logic is amiss. I originally got this answer incorrect, and as I am doing my review I came to this conclusion. But I would like to be corrected if there is soemthing I am not doing right. Thanks in advance.

[Adam Tyson]

Your logic here looks perfect, Aubrey! I think you just had a typo in the first premise - you had "Cat Outside" crossed out when it was the Sufficient Condition, but you immediately corrected it when you wrote the contrapositive. I've fixed that typo for you.

Well done, nice job!