Question 1
Anita says: 'Rohan has the gold coin'
Rohan says: 'I do not have the gold coin'
Kiran says: 'Anita is lying'
Can all these statements be true simultaneously?
Let's test if all statements can be true:
Assumption 1: If Anita tells truth, then Rohan has gold coin.
But Rohan claims not to have it - contradiction if Rohan tells truth.
If Rohan lies, then Rohan DOES have the item - consistent with Anita.
Then Kiran says Anita lies - but we assumed Anita tells truth - contradiction!
Assumption 2: If Anita lies, then Rohan does NOT have gold coin.
Rohan says the same thing - consistent if Rohan tells truth.
Kiran says Anita lies - consistent if Kiran tells truth.
Therefore, all statements CAN be consistent when Anita lies, Rohan and Kiran tell truth.
Thus, the statements are consistent.
Assumption 1: If Anita tells truth, then Rohan has gold coin.
But Rohan claims not to have it - contradiction if Rohan tells truth.
If Rohan lies, then Rohan DOES have the item - consistent with Anita.
Then Kiran says Anita lies - but we assumed Anita tells truth - contradiction!
Assumption 2: If Anita lies, then Rohan does NOT have gold coin.
Rohan says the same thing - consistent if Rohan tells truth.
Kiran says Anita lies - consistent if Kiran tells truth.
Therefore, all statements CAN be consistent when Anita lies, Rohan and Kiran tell truth.
Thus, the statements are consistent.