Last year, a software company held a contest to generate ideas for their new logo. According to the rules, everyone w...

on November 11, 2019


Hello, Why is the answer about necessary.


on November 12, 2019


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 on June 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