Consider the set of all twitter users In each part of this p

Consider the set of all twitter users. In each part of this problem we define a relation R on this set. Determine whether R is reflexive, symmetric, antisymmetric, and/or transitive: (a, b) elementof R if there are no common followers of a and b. (a, b) elementof R if there is a user c who is a follower of both a and b. (a, b) elementof R if every user who is a follower of a is also a follower of b.

Solution

a.) aRb if there is no common follower of a and b.

Not reflexive. i.e., a is not related to itself because those who are follower of frst a in (a,a) are also follower of second a in (a,a) since both are same.

Yes Symmetric. If a and b have no common follower then b and a also do not have common follower.

Not transitive : If a and b do not have common follower and b and c do not have common follower then it might happent hat a and c gets a common follower. Ex. If X follows a and not b whereas it follows c then a and c gets a common follower.

Not anitsymmety. If a and b have a common follower also b and a have a common follower then both the followers need not be same. i.e., X is follower of a and b whereas Y (distinct from X) is follower of b and a then X and Y are not same.

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b) Not reflexive. If i open an account i may not have any follower.so i am not related to myself. (Unless we assume that there is a condition that I cannot follow myself )

Yes Symmetric. If aRb that means there is a user c who is follower of both a and b that means c is also follower of b and a. Thus symmetric.

Not transitive: if there is user c who is follower of both a and b whereas there is user d who is follower of b and c then c and d need not be same i.e., there need be a follower for a and c.

Not antisymmetric: if there is user c who is follower of a and b and also there is follower for b and a then those 2 followers need not be same. (Not antsymemtric always!)

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c) Yes reflexive: If every user who is follower of a that means it is also a follower of a i.,e aRa.

Not symmetrc: If aRb i.,e every user that is follower of a is also follower of b but converse may not be true i.,e followers of b need not be followers of a.

Yes transitieve: if aRb and bRc i.,e every user who is follower of a is also follower of b and every user who is follower of b is also follower of c . Hence , every user who is follower of a is also follower of c.

Yes aintsymmetric: If aRb and bRa i.e., every user who is follower of a is follower of b and every user who is follower of b is follower of a that means the set of followers are same.