12. Show that the relation R defined in the set A of all triangles as R={(T1,T2) : T1 is similar to T2}, is equivalence relation. Consider three right angle triangles T1 with sides 3,4,5, T2 with sides 5,12,13 and T3…
11. Show that the relation R in the set A of points in a plane given by R={(P,Q) : distance of the point P from the origin is same as the distance of the point Q from the origin}, is…
10. Give an example of a relation. Which is: (i) Symmetric but neither reflexive nor transitive. (ii) Transitive but neither reflexive nor symmetric. (iii) Reflexive and symmetric but not transitive. (iv) Reflexive and transitive but not symmetric. (v) Symmetric and…
9. Show that each of the relation R in the set A={x(in)Z : 0≤x≤12}, given by (i) R={(a,b) : |a–b| is a multiple of 4} (ii) R={(a,b) : a=b} is an equivalence relation. Find the set of all elements related…
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…
