Question

Search ll 19:15 1.) (a) binomial relation on N x N Define as (a, b) (c, d)<a + d = b + c Is this binary relation is equivalent relation? If there is an equivalence relation, write three elements of the equivalence class (5,2) to be represented (B)A binary relation on N x N is defined as follows. (a, b)(c, d) a+d<=b + c Will this binary relation be a partial order relation? If it is a partial order relationship, is this relationship total order? C.) What relationship holds between the Fibonacci numbers Fn and Fn-2 Fn+2? Predict it, write it as a proposition, and prove that the proposition is correct D.) (McCarthy's 91 function) Function M: Let N Z be a function that is defined recursively (10 points) as follows if n> 100, M (n) =n-10 if n <100, M (M (n 11) Then M (100) M (M (111) M (101) 91. + + determine: (a) M (99) and M (101) (b) For any integer n>=1, consider what the value of M (n) would be.

Answer 1

Though questions are written as subpart of one question but they all are full-fledged question on their own, so solving more than one is not possible I request you to post separately for each question

Solution to part A

(a, b) To cheen uahuthen i* t^ equvalut Refteriue Ca,)~(a6) iyme'c Ctb then (Ca)4i6) caib 1d) tet. (aib) (Cid) ") Tyaми Hue at d C-d a-b (Cid)e) -d e-f ' e-f a-b = atf -e tb ca,b) e 1f ). Bo aolation is equivalur e eebton to ue thece evalene oloss element e 5,2) (5,2)(,) (S,2)(6, 2 (S,2) (7,4

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