If R is a relation on the set {a, b, c} defined by R = {(a, b), (b, c)}, which p

If R is a relation on the set {a, b, c} defined by R = {(a, b), (b, c)}, which property does R NOT have?

If R is a relation on the set {a, b, c} defined by R = {(a, b), (b, c)}, which property does R NOT have?

Step 1: Understand what a relation is. A relation R on a set is a collection of ordered pairs from that set.
Step 2: Identify the set we are working with, which is {a, b, c}.
Step 3: Look at the relation R given, which is R = {(a, b), (b, c)}.
Step 4: Check if R is reflexive. A relation is reflexive if every element is related to itself. Here, (a, a), (b, b), and (c, c) are not in R, so R is not reflexive.
Step 5: Check if R is symmetric. A relation is symmetric if for every (x, y) in R, (y, x) is also in R. Here, (b, c) is in R, but (c, b) is not, so R is not symmetric.
Step 6: Check if R is transitive. A relation is transitive if whenever (x, y) and (y, z) are in R, then (x, z) must also be in R. Here, (a, b) and (b, c) are in R, and (a, c) is not in R, so R is not transitive.
Step 7: Conclude which properties R does not have. R is not reflexive, not symmetric, and not transitive.

Relation Properties – Understanding the properties of relations, including reflexivity, symmetry, and transitivity.
Set Theory – Basic knowledge of sets and how relations are defined on them.