Please read and answer the following: In your response, clearly label answers wi
ID: 3571780 • Letter: P
Question
Please read and answer the following:
In your response, clearly label answers with a, b, c, and d. Remember to justify your answers when requested. Define the relation R on the set A = {1, 7, 21, 35, 36} as: (a, b) e R if GCD (a.} 6) > 1 (GCD is the Greatest Common Divisor) a. Find three distinct paths from node 36 to node 35. (Use the rightarrow symbol to indicate a transition between nodes.) b. Is R reflexive? Justify your answer. c. Is R symmetric? Justify your answer. d. Is R transitive? Justify your answer.Explanation / Answer
Define the relation R on the set A ={1,7,21,35,36} as
If GCD(a,b) >1(GCD is the Greatest Common Divisior)
Solution:
If GCD (a,b) >1(GCD is the Greatest Common Divisior) then
Prime factors of 36 are 1,2,3,4,9,12,18,36
prime factors of 35 are 1,5,7,35
GCD(35,36) is 1
21->36
36->36
If distnict paths means every node appears only once, from the above taken two examples only for to know about distnict paths from node 36 to 35.
(b) Is R reflexive ? Justify your answer
Solution:
The statement “Is R reflexive” is True.
· Here (a, a) € R, for all a € A which means every element of A is R related to itself.
· a R a for every a € A.
So R is reflexive.
(c) Is R symmetric? Justify your answer
Solution:
The statement “Is R symmetric” is False.
· That means R is anti symmetric relation, it can be described as below way.
· If (a,b) € R then (b, a) €R because GCD(a,b)=GCD(b, a).This relation is in partial order. Partial order relations are anti symmetric.
(d) Is R transitive? Justify your answer
Solution:
The statement “Is R transitive” is False.
· Some elements in the Set A must not hold the property.
· Like a €b and b€c than a€c
So R is not transitive.
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