Category Relations

8. Show that the relation R in the set A={1,2,3,4,5} given by R={(a,b) : |a–b| is even}, is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are…

7. Show that the relation R in the set A of all the books in a library of a college, given by R={(x,y) : x and y have same number of pages} is an equivalence relation. Relations and Functions Exercise…

6. Show that the relation R in the set {1,2,3} given by R={(1,2), (2,1)} is symmetric but neither reflexive nor transitive. Relations and Functions Exercise 1.1 Previous Next Class 12 Relations and Functions Exercise 1.1 1. Determine whether each of…

5. Check whether the relation R in R defined by R={(a,b) : a≤b3} is reflexive, symmetric or transitive. Relations and Functions Exercise 1.1 Previous Next Class 12 Relations and Functions Exercise 1.1 1. Determine whether each of the following relations…

4. Show that the relation R in R defined as R={(a,b) : a≤b}, is reflexive and transitive but not symmetric. Relations and Functions Exercise 1.1 Previous Next Class 12 Relations and Functions Exercise 1.1 1. Determine whether each of the…

3. Check whether the relation R defined in the set {1,2,3,4,5,6} as R={(a,b) : b=a+1} is reflexive, symmetric or transitive. Relations and Functions Exercise 1.1 Previous Next Class 12 Relations and Functions Exercise 1.1 1. Determine whether each of the…

2. Show that the relation R in the set R of real numbers, defined as R={(a,b) : a≤b2} is neither reflexive nor symmetric nor transitive. Relations and Functions Exercise 1.1 Previous Next Class 12 Relations and Functions Exercise 1.1 1.…

1. Determine whether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A={1,2,3,…,13,14} defined as R={(x,y) : 3x–y=0} (ii) Relation R in the set N of natural numbers defined as R={(x,y) : y=x+5…