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