In a room there are only two types of people, namely Type 1 and Type 2. Type 1 people always tell the truth and Type 2 people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell him to toss it and hide the result from you till you ask for it. Upon asking the person replies the following “The result of the toss is head if and only if I am telling the truth” Which of the following options is correct?
A. The result is head
B. The result is tail
C. If the person is of Type 2, then the result is tail
D. If the person is of Type 1, then the result is tail
Case 1: if the person is Type 1 person then
The result of the toss is head if and only if I am telling the truth
denote it by (P↔Q)
P : The result of the toss is head
Q: I am telling the truth
“I am telling the truth” is true for him. (yes, he always tells the truth)
his statements are always true, so (P↔Q) must be true.
So P is also true.
P↔Q = TRUE—(1)
Q = TRUE—(2)
P↔TRUE = TRUE ( 2 is substituted in 1)
P is TRUE
Case 2: if the person is Type 2 person then
P↔Q is false (yes, he is always false)
and more over Q is false as it is also said by him.
P↔Q = FALSE—(1)
Q = FALSE—(2)
P↔FALSE = FALSE ( 2 is substituted in 1)
P is TRUE