Problem #PRU-100437

Problems Discrete Mathematics Set theory and logic Mathematical logic

Problem

a) Twelve inhabitants are sitting under a big tree. One of them says, “There is at least one liar among us”. How many knights can be among them?

b) A different group of other twelve inhabitants is resting by the river. Suddenly, one of them exclaims, “If everyone except me is a liar, then I am a liar too”. How many liars can be among them?