Problem:
Question 1: What is set theory? Explain thoroughly.
Question 2: Prove or disprove: A ? (B ? C) = (A ? B) ?(A ? C) Using Set Identities (Table 1).
Question 3: Prove that A ? (B ? C) = (A ? B)?(A ? C) By giving a proof through set builder notation and using logical equivalence.
Question 4: Prove that (A \cup B)\cap C \subset A \cup (B\cap C) for any three sets A, B, and C.
Please prove the following questions.