Question: Problem 2. On P(N), consider the relation E= {(A, B) P(N)? | (AAB) N {2023,2024} = @}. [Recall: the symmetric difference is defined by AAB

Problem 2. On P(N), consider the relation E= {(A, B) P(N)? | (AAB) N {2023,2024} = @}. [Recall: the symmetric difference is defined by AAB = (A\\ B) U (B \\ A).] (a) Prove that E is an equivalence relation on P(N). (15 pt.) (b) How many elements are there in the set P(N)/E? Provide a system of representatives for E. No proof required. (20 pt.) [Instructions: your answer should look like "P(N)/E has ... elements, and a system, of representatives is given by ...."]

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