I'm having trouble representing these questions in a propositional logic formula:
Alice, Bob and Claire want to attend the CPS I lecture. The exercise groups are almost full, only group 1 and group 2 have places left.
(a) If Alice joins group 1, the tutor refuses to accept Bob because they always talk.
(b) At least one of Bob and Claire cannot go to group 1, as they lead a chess group together that meets at the same time.
(c) Claire hates Alice and doesn’t want to be in the same group.
(d) Alice wants to submit the solutions with either Bob or Claire and thus needs to be in a group with this person.
Model the above statements in propositional logic where the atomic propositions:
a(Alice), b (Bob), c (Claire) are assigned the value true if the corresponding person joins group 1, and false else.
Which persons join which group? Use a truth table to find out.
Here is my solution:
(a) a -> b
(b) ¬(b ^ c)
(c) a -> ¬c
(d) (a ^ b) xor (a ^ c)
I don't think the solutions are correct. What do you think what changes should I make?
How to find out which persons join which group using the truth table?
Thank you :)