Discrete math Which of the following zeroone matrices are eq

Discrete math

Which of the following zero-one matrices are equivalent relations? [1 0 0 1 1 1 1 0 0] [1 1 1 0 1 1 1 1 1] [1 0 10 0 1 0 1 1 0 10 0 1 0 1] [1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1]

Solution

A is not an equivalence relation as it is not Reflexive.

B is not an equivalence relation as it is Reflexive but not symmetric.

C and D- It is Reflexive, Symmetric and Transitive (All pairs that fit transitive pattern (a, b) ^ (b, c) include or imply a pair on diagonal which are always valid such as (1, 3) ^ (3, 1) -> (1, 1))

It is an equivalence relation because it is reflexive, symmetric, and transitive.