When planning a party you want to know whom to invite. Among the people you would like to invite are three touchy friends. You know that if Jasmine attends, she will become unhappy if Samir is there, Samir will attend only if Kanti will be there, and Kanti will not attend unless Jasmine also does. Which combinations of these three friends can you invite so as not to make someone unhappy?

Question

Mathematics

Selina Maynard

2 September, 02:31

When planning a party you want to know whom to invite. Among the people you would like to invite are three touchy friends. You know that if Jasmine attends, she will become unhappy if Samir is there, Samir will attend only if Kanti will be there, and Kanti will not attend unless Jasmine also does. Which combinations of these three friends can you invite so as not to make someone unhappy?

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Answers (1)

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Rachael · Answer 1

Jasmine only.

Jasmine and Kanti only.

No one.

Step-by-step explanation:

There is no possible way to invite all three friends.

Since both Samir and Kanti will not attend if someone else is not invited, Jasmine is the only friend that can be invited on her own:

One person: Jasmine.

When inviting two people, if Jasmine is invited, Samir can't be invited and Kanti will only attend if Jasmine also does. Therefore, Jasmine and Kanti can go together and there is no way Kanti can be invited.

Two people: Jasmine and Kanti.

Furthermore, if nobody is invited, no one will be unhappy.