The relation T is

Question

“n/m” means that n is a factor of m, then the relation T is

(a) reflexive and symmetric

(b) transitive and symmetric

(c) reflexive, transitive and symmetric

(d) reflexive, transitive and not symmetric 

Ans: option (d) But how ?

Answer 1

For relation to be symmetric if (m,n) belong to R then (n,m) also belongs to R ie m is factor of n and n is factor of m this is possible only when m=n this relation is antisymmetric  for eg(2,4) belongs to R but (4,2) does not belong to r so ans is d

Comments

Then how this is reflexive ?

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every no. divide itself. like n/n.

Answer 2

Suppose u have elemens like below ways ::
R={(1,2)(2,1)}

2%1==0 but 1%2!=0 that's why A relation with "\" will never be symmetric but it is obvious that it will be by the definition of the reflexive and transitive u will get a relation "\" will be both as previous.

Answer 3

n is the factor of m. n is also the factor of itself similarly for m then it is reflexive.

n is the factor of m but it is not necessary that m is the factor of n, it can only possible when n=m, so it is not symmetric.

and if m/l then it implies n/l then it is transitive

so the answer is d it is reflexive, transitive but not symmetric