The binary relation R = {(1,1),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(4,1),(4,2)} on the set A = {1,2,3,4} is:
A. reflexiv...

Question

The binary relation R = {(1,1),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(4,1),(4,2)} on the set A = {1,2,3,4} is:
A. reflexive, symmetric and transitive
B. neither reflexive, nor irreflexive but transitive
C. irreflexive, symmetric and transitive
D. irreflexive and antisymmetric

Accepted Answer

B. neither reflexive, nor irreflexive but transitive We need to check reflexivity (does every element relate to itself?), irreflexivity (does NO element relate to itself?), symmetry (if aRb then bRa?), and transitivity (if aRb and bRc then aRc?) for the given explicit set of pairs. Notice (1,1) is in R (so not irreflexive), but (3,3) and (4,4) are missing (so not reflexive). Since R is neither reflexive nor irreflexive, we check transitivity and confirm it holds.

The binary relation R = {(1,1),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(4,1),(4,2)} on the set A = {1,2,3,4} is: A. reflexive, symmetric and transitive B. neither reflexive, nor irreflexive but transitive C. irreflexive, symmetric and transitive D. irreflexive and antisymmetric