Can you please solve these 5 problems thank you

11. Prove or provide a counterexample. Let A = {a1, a2, a3, a4} and B = {b1, b2, b3}. Define f : A -> B by f(a1) = b1, f(a2) = b1, f (a3) = b2, and f (as) = b2. (a) Is f a function? Why or why not? Explain. (b) Is f one-to-one? Why or why not? Explain. (c) Is f onto? Why or why not? Explain. (d) What is the preimage of b3 under f? What is the preimage of b2 under f? (e) What is f-(B)? What is f(A)?12. a. Give an example of a relation that is transitive but not reflexive and not symmetric. Explain why your example meets all of the conditions. b. Give an example of a relation that is reflexive and symmetric but not transitive. Explain why your example meets all of the conditions.13. Prove or provide a counterexample. For all (m, n) E Z x Z, let R be defined on Z x Z by: m Rn # 4 | (m - n). Show that R is an equivalence relation on Z x Z. What are the equivalence classes?14. Use the RSA cipher with public key it = 667 = 23 - 29 and e = 41. Encode the message into its numeric equivalent and encrypt it: MATH. \f