Can I get an example of a program in Rust that implements the following function, Each of these functions should be created with a functional programming style (no side effects, no global values, immutable variables, etc.). Implement the managing code in any style.

Reflexive

Input: a list of pairs, L, and the set S over which the relation is defined. Interpreting the input as a binary relations, return True if it is reflexive and False otherwise.

Symmetric

Input: a list of pairs, L, and the set S over which the relation is defined. Interpreting the input as a binary relation, return #T if it is symmetric and False otherwise.

Transitive

Input: a list of pairs, L. Interpreting the input as a binary relation, return True if it is Transitive and False otherwise.

Antisymetric

Input: a list of pairs, L. Interpreting the input as a binary relation, return True if it is Transitive and False otherwise.

Equivalence

Input: a list of pairs, L. Interpreting the input as a binary relation, return True if it is an equivalence relation and False otherwise