The correct answer is Option (A).
Symmetric: aRb => bRa
x is a brother of y. So x should be brother of x which is not necessary. y might be a sister of x.
Therefore, R is not symmetric relation.
Transitive: aRb and bRc imply aRc
x is a brother of y, y is a brother of x, but x is not a brother of x.
Therefore, R is not a transitive relation.
Equivalence: The relation must be reflexive, transitive, and symmetric.
But, R is not satisfied with any of the 3 relation properties.
Therefore, R is not an equivalence relation.
Partial Order: The relation must be reflexive, transitive, and anti-symmetric.
But, the R is neither reflexive nor transitive.
Therefore, R is not a partial order relation.
So, the correct answer is NO, NO, NO, NO.