Lets take A ={1,2,3,4}
R will be = {(1,1),(2,2),(3,3),(4,4)} as minimum elements
S will be = {(1,1),(2,2),(3,3),(4,4)} as minimum elements
(a) R∪S is reflexive:True since, it will defiantly contain {(1,1),(2,2),(3,3),(4,4)}.
(b) R∩S is reflexive: True since, it will defiantly contain {(1,1),(2,2),(3,3),(4,4)}.
(c) R⊕S is irreflexive: Since common elements in both R and S {(1,1),(2,2),(3,3),(4,4)} will be removed , Which is basic requirement of Reflexive relation , Hence, irreflexive .
(d) R−S is irreflexive: Since common elements in both R and S {(1,1),(2,2),(3,3),(4,4)} will be removed , Which is basic requirement of Reflexive relation , Hence, irreflexive .
(e) SoR is reflexive: will contain {(1,1),(2,2),(3,3),(4,4)} Which is basic requirement of Reflexive relation , Hence, Reflexive .