Types OF relation ( Reflexive,Symmetric,Transitive, Equivalenc& Anti Equivalence) & illustartion

Explain the Relation (i) Reflexive (ii)Symmetric(iii) Transitive

check whether the relation R in the set N of natural numbers given by R = { (a,b) : a is divisor of b } is reflexive, symmetric or transitive. Also determine whether R is an equivalence relation

The relation R in R defined as R={(a,b):a (A) Reflexive and symmetric (B) Transitive and symmetric (C) Equivalence (D) Reflexive,transitive but not symmetric

Let R be a relation defined on the set of real numbers by aRb hArr1+ab>0 then R is (A) Reflexive and symmetric (B) Transitive (C) Anti symmetric (D) Equivalence

Let R be a relation defined by R={(a,b):a>=b,a,b in R}. The relation R is (a) reflexive,symmetric and transitive (b) reflexive,transitive but not symmetric ( d) symmetric,transitive but not reflexive (d) neither transitive nor reflexive but symmetric

R is a relation on the set Z of integers and it is given by (x ,\ y) in RhArr|x-y|lt=1. Then, R is (a) reflexive and transitive (b) reflexive and symmetric (c) symmetric and transitive (d) an equivalence relation

The relation has the same father as' over the set of children (a) only reflexive (b) only symmetric (c) only transitive (d) an equivalence relation

Check whether the relation R in the set Z of integers defined as R={(a,b):a +b is divisible by 2} is reflexive, symmetric or transitive. Write the equivalence class containing 0 i.e. [0].

Let A={1, 2, 3) be a given set. Define a relation on A swhich is (i) reflexive and transitive but not symmetric on A (ii) reflexive and symmeetric but not transitive on A (iii) transitive and symmetric but not reflexive on A (iv) reflexive but neither symmetric nor transitive on A (v) symmetric but neither reflexive nor transitive on A (vi) transitive but neither reflexive nor symmetric on A (vii) neither reflexive nor symmetric and transitive on A (vii) an equivalence relation on A (ix) neither symmetric nor anti symmmetric on A (x) symmetric but not anti symmetric on A

An integer m is said to be related to another integer n if m is a multiple of n. Then the relation is: (A) reflexive and symmetric (B) reflexive and transitive (C) symmetric and transitive (D) equivalence relation