A group of 6 friends - Adam, Barbara, Sam, Cohen, Denise, and Kate have been invited to a job interview at Company X. At least two people must accept their invites. Each of their decision to either go or not go is dependent on the following conditions:
Cohen goes if both Denise and Kate go.
Barbara goes if Adam does not go.
Kate does not go only if Sam goes.
At least one of Adam and Kate do not go.
Which of the following is always true given the above restrictions?
Both Adam and Kate do not go
Sam goes if Adam goes
Barbara goes if Sam goes
At least one of Barbara and Cohen go
Cohen goes if Denise goes