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