Define the following terms and give some examples: relation, symmetric relation, transitive relation, reflexive relation, and equivalence class.

Relations in Mathematics | Antisymmetric, Asymmetric & Symmetric

Determine whether each of the following relations are reflexive, symmetric and transitive:(i) Relation R in the A = left{1, 2, 3, ..., 13, 14right} defined as R = left{(x, y) : 3x - y = 0right}(ii) Relative R in the N of natural numbers defined as R=left{(x, y):y=x 5 text{and} x < 4right}(iii) Relation R in the A=left{1, 2, 3, 4, 5, 6right} as R=left{(x, y):y text{is divisible by} xright}(iv) Relative R in the Z of all integers defined as R=left{(x, y):

Let A = 1,2,3,4 and R a relation on whose matrix is MRDetermine whether R is reflexive; irreflexive; symmetric; asymmetric; antisymmetric; transitive Show your work)