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?
Okay, this problem gives three different facts that express the relationship between things occuring/being true; and here is how I translated them
(1) If Samir attends the party, then Jasmine will be unhappy.
(2) If Samir attends the party, then Kanti will be there.
(3) If Kanti attends the party, then Jasmine must also attend the party.
I correctly translated (1) and (3); however, the answer key claims that (2) should be written as
(2) If Kanti attends the party, then Samir must attend the party.
This does not seem consistent with the answers I received here. If I read the posts correctly, $p$ only if $q$ translates to $p \implies q$
Best Answer
Denote by $P_X$ the proposition that person $X$ will attend the party. Then from the story we conclude that $$P_S\Rightarrow P_K\Rightarrow P_J\Rightarrow\neg P_S\ .\tag{1}$$ This chain implements in turn "$S$ will be there only if $K$ is there", "$K$ will not attend unless $J$ does", and "$J$ will not attend if $S$ does".
One of $P_S$ and $\neg P_S$ is true, so there is a first term in $(1)$ which is true. $P_S$ can definitely not be true. When $P_K$ is true, $K$ and $J$ attend; when $P_J$ is the first true term only $J$ attends, and when $\neg P_S$ is the first true term none of the three attends.