lets assume A = {1,2,3,4}
Given that, A relation is said to be triangular iff aRb and cRb ==> aRc for all a,b,c belongs to A
Option A, B) S = {(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)} ===> equivalence relation.
Now we have to check whether it is reflexive and triangular relation
{(1,1),(2,2),(3,3),(4,4)} ====> reflexive relation.
(1,1), (2,1) ==> (1,2) is present in S
(2,2), (1,2) ==> (2,1) is present in S
so it is triangular relation.
option A ,B) is True.
Option C) S = {(1,2),(2,1),(2,2)} is symmetric and triangular relation.
how triangular relation is shown below
(1,2), (2,2) ==> (1,2) is present in S
(2,2), (1,2) ==> (2,1) is present in S
But S is not transitive relation. (1,2),(2,1) ==> (1,1) is missing
option C) should be False.
Option D) S = {(4,2),(2,1),(4,1),(2,4)} is transitive and triangular relation.
but not symmetric relation. (1,2), (1,4) are missing.
Option D) should also be False.