Let's identify the sufficient and necessary conditions in the second sentence.
If someone entered the contest (EC), then they received a T-Shirt (TS).
EC - - - - - - - - - - > TS suf nec
This allows us to create a contrapositive. If someone did not win a T-shirt, then they did not enter the contest. We can say this for certain. If the necessary condition fails, then so does the sufficient condition.
not TS - - - - - - - - -> not EC suf nec
Now, let's evaluate the conclusion. Juan has a T-shirt with the company's new logo, so he must have entered the contest.
TS - - - - - - - - - > EC is not valid. suf nec
We cannot simply reverse our sufficient and necessary conditions. It takes on an entirely new meaning. It states that Juan owning the T-shirt proves that he entered the contest. However, there could be a number of ways to acquire a T-shirt. Maybe Juan bought it, or maybe it was given to him by someone who entered the contest. This is why B is the correct answer. The author concludes that entering the contest is a necessary condition, when the premise indicates that it is sufficient.
Gabriela-DiazJune 29, 2020
I understand this question but in the past I have noticed I get confused sometimes if there is a question and I know it is a necessary sufficient mix up , but in the answer choices there are two options that deal with it: For example, takes a condition that is sufficient for a particular outcome as one that is necessary for that outcome vs takes a condition that is necessary for a particular outcome as one that is sufficient for that outcome. I would get confused as to which one to pick. Can you explain to me the difference between these? Is the first a incorrect reversal and the second a incorrect negation? Please use this question as a way to illustrate the difference. Thank you
