Which Graph Represents This Equation? [tex]y=\frac{3}{2}x^{2}-6x[/tex]I Know The Answer Is C. What I
The relation R on the set of natural numbers (N) is defined as (a, b) ∈ R if and only if a/b is a natural number. This relation exhibits the properties of reflexivity, symmetry, and transitivity.
Reflexivity: For any natural number a, a/a = 1, which is a natural number. Therefore, (a, a) ∈ R for all a ∈ N. Hence, R is reflexive.Symmetry: If (a, b) ∈ R, then a/b is a natural number. This implies b/a is also a natural number since the division is commutative. Thus, (b, a) ∈ R. Therefore, R is symmetric.
Transitivity: Let (a, b), (b, c) ∈ R, which means a/b and b/c are natural numbers. As the division operation is closed under natural numbers, a/c = (a/b) * (b/c) is also a natural number. Therefore, (a, c) ∈ R, and R is transitive. In summary, the relation R on the set of natural numbers is reflexive, symmetric, and transitive, making it an equivalence relation.
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