This Reduction is trying to prove that 2CNF-SAT is also NP-Complete, after proving 3CNF-SAT is NP-Complete.
If we had a reduction that given an instance of 2CNF-SAT with k clauses over 'i' number of variables, and we create an instance of 3CNF-SAT with 2n clauses by introducing for clause i a new variable y; then for the i'th 2SAT clause we generate two 3SAT clauses. This is a reduction from a 2CNF-SAT to a 3CNF-SAT.
Is this not a correct reduction because all of the other clauses after the transformation are still 2CNF-SAT except for the i'th clause?