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Q) 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 ?

Although the question has already been answered here and here but I am not satisfied with it. I am getting the answer as none should be invited for a party. Please check my work and if anything is wrong then please correct it.

My attempt :-
Since $3$ statements are there :-
$1)$ If Jasmine attends, she will become unhappy if Samir is there.
$2)$ Samir will attend only if Kanti will be there.It means if Samir attend the party then Kanti will also attend.
$3)$ Kanti will not attend unless Jasmine also does. It means if Kanti attend the party then Jasmine will also attend it.

Now, I consider $2$ cases as :-
$1)$ Jasmine attends the party
Now, If Samir does not attend the party then Jasmine may or maynot be happy. i.e. If Samir is not there then Jasmine may be happy and may not be happy. So, both possibilities are there.
Now, if Samir does not attend the party then Kanti may or may not attend the party.
$\rightarrow$ If Kanti attends the party then Jasmine also does. So, In party,if Jasmine and Kanti are there then Jasmine may be happy and may not be happy as I said earlier.
$\rightarrow$ If Kanti does not attend the party then Jasmine may or may not attend. Suppose, Samir and Kanti does not attend the party and only Jasmine attends but Jasmine may or may not be happy.

$2)$ Jasmine does not attend the party
Now, Samir may or may not attend the party. If Samir attends then Kanti attends and then Jasmine will also attend it. So, It is not a possible case. Now, if Samir does not attend then Kanti may or may not attend but if Kanti attends then Jasmine should also attend. So, It is not possible. Only possibility is none of the $3$ attend the party.

So, I am getting that when none of 3 should attend the party.If anything is wrong then please correct me. Thank you.

ankit
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  • At a glance, Samir is the problem. If Samir is out, then Jasmine can come and so can Kanti. – lulu May 28 '19 at 13:48
  • If Jasmine alone attends the party, none of the conditions are violated. You say she "may or may not be unhappy" but the question means she will not be made unhappy by violation of one of the three rules. – saulspatz May 28 '19 at 13:49
  • Question says "she will become unhappy if Samir is there" . It means if Samir is not there then she may or may not be unhappy. In $p \rightarrow q$ , if p is false then q may be true or false. In both cases, whole statement is true. Can you please tell me, Am I missing something ? @saulspatz , @ lulu – ankit May 28 '19 at 13:57
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    You are misinterpreting the problem. It talks about your making someone unhappy by violating the rules. There are all kinds of other reasons why these girls may be unhappy, but they have nothing to do with the case. – saulspatz May 28 '19 at 14:10
  • Thank you :) @saulspatz – ankit May 28 '19 at 14:36
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    Invite all your friends. Touchyness is their problem, not yours. – William Elliot May 28 '19 at 22:39

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