i am required t complete question 1 parts A,B and C

A,Arithmetic proof 4 Points Prove that there exist no different positive integers m and y such that m/y2 : mg/y. @ Please select filefs} Select file[s) B . Arithmetic proof with summation 6 Points Define the sequence so, 31, 52. . .. by so : 1 and a}; : EH}; 33- for all integers k Z_> 1. Prove that 5.. : 2\"_1 for all n 3 3. @ Please select filefs} Select file[s) C. Set theory 9 Points Prove the identity A (B (I) : (0 Fl A) LJ (A B) in two ways. Once by means of the element method, and once algebraically. For the algebraic proof you may use (only) the set identities from Epp Theorem 6.2.2, as shown in the figure below. Theorem 6.2.2 Set Identities Let all sets referred to below be subsets of a universal set U. 1. Commutative Laws: For all sets A and B, (a) AUB = BUA and (b) AnB = BnA. 2. Associative Laws: For all sets A, B, and C, (a) (A UB) UC = AU(BUC) and (b) (An B) nC = An (BnC). 3. Distributive Laws: For all sets, A, B, and C, (a) AU(BOC) = (AUB) n(AUC) and ( b ) An ( B UC) = ( An B ) U ( An C). 4. Identity Laws: For all sets A, (a) A UO = A and (b) AnU = A. 5. Complement Laws: (a) A UA = U and (b) AnAc = 0. 6. Double Complement Law: For all sets A, (AC)c = A. 7. Idempotent Laws: For all sets A, (a) A UA = A and (b) An A = A. 8. Universal Bound Laws: For all sets A, (a) AUU = U and (b) And =0. 9. De Morgan's Laws: For all sets A and B, (a) (AUB) = AnBC and (b) (AnB) = ACUB. 10. Absorption Laws: For all sets A and B, (a) AU(AnB) = A and (b) An (AUB) = A. 11. Complements of U and 0: (a) UC = 0 and (b) 0 = U. 12. Set Difference Law: For all sets A and B, A - B = AnBC