1. 1. write the following based upon the following conditional statement: if company a does capacity planning, company a will have optimized it services. a. converse b. inverse c. contrapositive 2. supposef: z-z is defined by f (x) = 2x2+1. a. explain using the definition of onto functions why the function f is or is not an onto function. b. explain using the definition of one-to-one functions why the functionf is or is not a 1-1 function. 3. consider the relation r on the set s = {1, 2, 3, 4} defined by r {(1,2), (1,3), (1, 4), (2, 1), (3,1), (3, 4), (4,1), (4,2)} a. explain why r is or is not symmetric. b. explain why r is or is not antisymmetric. c. explain why r is or is not reflexive. 4. suppose a = {1, 2, 3, 4}. let s and r be relations on a defined as follows: s {(1, 1), (1, 3), (2, 3), (3, 4), (4,1)} r {(1, 4), (2, 2), (3, 2), (4, 2)} write down the set of pairs in s o r.