Let x = { x elementof z^+: x lessthanorequalto 100]: that is, x is the set of all integers from l to 100. for each y elementofmiddotp(x) we define a_y = {z elementof p(x): y and z have the same number of elements) (a) prove that(a_y: y elementof p(x)} partitions p(x). (b) let ~ denote the equivalence relation on p(x) that is associated with this partition (according to theorem 11.4). if possible, find a, b, and c such that 1. a ~ {1, 2, 3} and a notequalto {1, 2, 3} 2. b not similar to {7, 8, 9} 3. c ~ x and c notequalto x.