EASY
12th ICSE
IMPORTANT
Earn 100

Determine whether each of the following relations are reflexive, symmetric and transitive: R={(a,b):a,b∈R,a≤b}.

Important Questions on Relations and Functions

MEDIUM
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 1 - Relations and Functions>EXERCISE 1.1
Let T be the set of all triangles drawn in a plane with R as a relation in T given by R=T1,T2:T1≡T2. Show that R is an equivalence relation.
EASY
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 1 - Relations and Functions>EXERCISE 1.1
Show that the relation R in the set A of all books in a library of a school, given by R={(x,y):x and y have same number of pages}, is an equivalence relation.
MEDIUM
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 1 - Relations and Functions>EXERCISE 1.1
Show that the relation R on the set I of all integers defined by R={(a, b): a-b is divisible by 3,a,b∈1} is an equivalence relation.
MEDIUM
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 1 - Relations and Functions>EXERCISE 1.1
Prove that the relation R in the set A= (5,6,7,8,9}, given by R={(a,b):a-b is divisible by 2}, is an equivalence relation. Find all elements related to element 6.  
EASY
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 1 - Relations and Functions>EXERCISE 1.1

Give examples of relations which are symmetric but neither reflexive nor transitive.

EASY
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 1 - Relations and Functions>EXERCISE 1.1
Give examples of relations which are transitive but neither reflexive nor symmetric.
MEDIUM
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 1 - Relations and Functions>EXERCISE 1.1
Give examples of relations which are symmetric and transitive but not reflexive.
EASY
12th ICSE
IMPORTANT
Understanding ISC Mathematics Class 12 Volume 1>Chapter 1 - Relations and Functions>EXERCISE 1.1

Give examples of relations which are symmetric and reflexive but not  transitive.