Correct Answer - C
The relation S is defined on the set of integers Z and xSy, if integer x divides integery.
Reflexive : Since, every integer divides itself
`therefore` integer x divides integer x
implies xSx
Hence, S is reflexive.
Symmetric : Let `x, y in Z` such that xSy
i.e., integer x divides integer y
Now, this does not implies that integer y divides integer x.
e.g. Take x = 2 and y = 4
Then, 2 divides 4 but 4 does not divides 2.
Thus, S is not symmetric.
Transitive : Let `x, y, z in Z` such that xSy and ySz.
implies integer x divides integer y and integer y divides integer z
implies integer x divides integer z
implies xSz
Hence, S is transitive.
