Kenneth Rosen Edition 7 Exercise 1.2 Question 18 (Page No. 23)

Question

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?

I was trying by converting the english language to logical equivalent statments.
j-> not s
s->k
not j -> not k
How to approach this question?

Answer 1

As given in question, we have three friends (J, S, K) & Everyone has two possibilities either Present or Absent. 

So, using this data we can make total $2^3=8$ combinations. 

by translating given english statements into logical statements. we have three logical statements, 

(J$\rightarrow\neg$S), (S$\rightarrow$K), ($\neg$J$\rightarrow\neg$K) . 

As we know that  (p$\rightarrow$q) is false only for p is True & q is False. we apply this rule on above three logical statements, 

Now result is, 

J is True $\rightarrow$ S is True -----(1)

S is True $\rightarrow$ K is False ----(2)

J is False $\rightarrow$ K is True ----(3)

 

by using this result we can easily eliminate false combination. 

Now, we make table for 8 combinations and eliminate false combination. Suppose, T=Present & F=Absent.

J	S	K
F	F	F
F	F	T	false(using 3rd logical statement).
F	T	F	false(using 2nd logical statement).
F	T	T	false(using 3rd logical statement).
T	F	F
T	F	T
T	T	F	false(using 1st or 2nd logical statement).
T	T	T	false(using 1st logical statement).

Remaining valid combinations for (J, S, K) are (F, F, F), (T, F, F), (T, F, T).

Hence, we can invite these three friends in above valid combinations, so as not to make someone unhappy. 

Comments

@Deepak Poonia Sir, please verify my answer.