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 Type 1" Which of the following options is correct?

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we do not know what is the person from whom those words are coming from, we can have two cases :

Truth-teller: definitely implies that result of toss is Head.Liar: The reality will be the negation of the statement.The negation of (x⟺y) is Exactly one of x or y holds. So, we negate the statement : "The result of the toss is head if and only if I am telling the truth". This gives rise to two possibilities:

Clearly, the second one cannot be true because it cannot be a Reality that the liar speaks the truth.

so, this implies that even if we negate the statement to see the reality or don't do that; The reality is that the toss yielded a Head.

answer = option B