Consider a binary relation on a set A has {a, b, c} 

A x A = { (a,a) (a,b) (a,c) (b,a) (b,b) (b,c) (c,a) (c,b) (c,c) }

Option a:  The smallest reflexive relation is {(a,a) (b,b) (c,c)}

True,  A relation R on set A is said to be reflexive, all diagonal relation have to present. So the smallest reflexive relation is {(a,a) (b,b) (c,c)} and The largest reflexive relation is { (a,a) (a,b) (a,c) (b,a) (b,b) (b,c) (c,a) (c,b) (c,c) }

Option b: The largest symmetric relation is {(a,a) (a,b) (a,c) (b,a) (b,b) (b,c) (c,a) (c,b) (c,c) }

True, The smallest symmetric relation is { } and The largest symmetric relation is { (a,a) (a,b) (a,c) (b,a) (b,b) (b,c) (c,a) (c,b) (c,c) }.

Option c: The largest equivalence relation is A x A.

True, An Equivalence relation is always Reflexive, Symmetric, and Transitive. The largest symmetric relation is { (a,a) (a,b) (a,c) (b,a) (b,b) (b,c) (c,a) (c,b) (c,c) } and it Reflexive, and Transitive. And it also  A x A relation.

Option d: The number of partially ordered relations on set A (1,2) is 5.

False, A relation is partially ordered relation iff Reflexive, Antisymmetric and Transitive. So the number of partaially ordered relations on set A is 3 are,

• {(1,1) (2,2)}
• {(1,1) (1,2) (2,2)}
• {(1,1) (2,2) (2,1)} 

So only d  is False.

Hence the correct answer is only d.