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

on November 11 at 10:24PM

Confused

Hello, Why is the answer about necessary.

1 Reply

on November 12 at 03:12AM

Hello @ca_teran1@yahoo.com,

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.