I have these 2 questions to prove or disprove confluence.
1)
Answer
2)
Answer
Now I am having difficulty understanding these. Aren't these 2 questions same? then why in one case it is confluent and not in the other case. Please correct me and help me understand this. Thank you.
No, the questions are not the same.
The first one asks for a proof that every element has at most one normal form.
The second one asks for a proof that every element has at least one normal form.
If there may be an element with no normal form at all, then the second claim is wrong (but the first one still has a chance).
If there may be an element with two different normal forms, then the first claim is wrong, but there is still hope for the second one.
And, by the way, neither question asks you to "prove (or disprove) confluence". The questions both ask you to assume as a given that $\succ$ is confluent and then asks whether this or that is a consequence of this assumption.