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