The binary relation R= { (1, 1), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3,…

To determine the properties of relation R on set A = {1, 2, 3, 4}, we check reflexivity, symmetry, and transitivity.

For reflexivity, every element must relate to itself: (1,1), (2,2), and (3,3) are in R, but (4,4) is missing. Thus, R is neither reflexive nor irreflexive.

For symmetry, if (a,b) is in R, then (b,a) must also be present. Here, (2,1) is in R but (1,2) is not, so it is not symmetric.

For transitivity, if (a,b) and (b,c) are in R, then (a,c) must be in R. Checking all pairs confirms this holds true for R. Therefore, the relation is transitive but neither reflexive nor irreflexive.