If R is a relation on the set A = {1, 2, 3} defined by R = {(1, 2), (2, 3), (3,

If R is a relation on the set A = {1, 2, 3} defined by R = {(1, 2), (2, 3), (3, 1)}, which of the following properties does R possess?

If R is a relation on the set A = {1, 2, 3} defined by R = {(1, 2), (2, 3), (3, 1)}, which of the following properties does R possess?

Step 1: Identify the set A, which is {1, 2, 3}.
Step 2: Identify the relation R, which is {(1, 2), (2, 3), (3, 1)}.
Step 3: Check if R is reflexive. A relation is reflexive if every element in A relates to itself. We need (1,1), (2,2), and (3,3) to be in R. They are not, so R is not reflexive.
Step 4: Check if R is symmetric. A relation is symmetric if for every (a, b) in R, (b, a) is also in R. We have (2, 3) in R, but (3, 2) is not in R, so R is not symmetric.
Step 5: Check if R is transitive. A relation is transitive if whenever (a, b) and (b, c) are in R, then (a, c) must also be in R. We have (1, 2) and (2, 3) in R, but (1, 3) is not in R, so R is not transitive.
Step 6: Conclude that R is not reflexive, not symmetric, and not transitive.

Reflexivity – A relation R on a set A is reflexive if every element in A is related to itself, meaning (a, a) is in R for all a in A.
Symmetry – A relation R is symmetric if for every (a, b) in R, the pair (b, a) is also in R.
Transitivity – A relation R is transitive if whenever (a, b) and (b, c) are in R, then (a, c) must also be in R.