If A = {1, 2, 3, 4 }, define relations on A which have properties of being: reflexive, transitive but not symmetric - Mathematics | Shaalaa.com

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):

Ex 1.1, 1 (i) - Relation R in the set A = {1, 2, 3 13, 14} defined as

Given an Example of a Relation. Which Is Reflexive and Symmetric but Not Transitive. - Mathematics | Shaalaa.com

Ex 1.1, 2 - Show R = {(a,b): a<=b2} is neither reflexive

Equivalence Relation

Ex 1.1, 5 - R = {(a, b) : a <= b3} is reflexive, symmetric

Write the Smallest Equivalence Relation on the Set A = {1, 2, 3} ? - Mathematics | Shaalaa.com