Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

The following relation is defined on the set of real numbers.

aRb if 1 + ab > 0

Find whether relation is reflexive, symmetric or transitive.

The following relation is defined on the set of real numbers.  aRb if |a| ≤ b

Find whether relation is reflexive, symmetric or transitive.

Prove that every identity relation on a set is reflexive, but the converse is not necessarily true.

If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, transitive but not symmetric ?

If A = {1, 2, 3, 4} define relations on A which have properties of being symmetric but neither reflexive nor transitive ?

If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, symmetric and transitive ?

Let R be a relation defined on the set of natural numbers N as
R = {(x, y) : x, y ∈ N, 2x + y = 41}
Find the domain and range of R. Also, verify whether R is (i) reflexive, (ii) symmetric (iii) transitive.

Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons.

An integer m is said to be related to another integer n if m is a multiple of n. Check if the relation is symmetric, reflexive and transitive.

Show that the relation '≥' on the set R of all real numbers is reflexive and transitive but not symmetric ?

Give an example of a relation which is reflexive and symmetric but not transitive?

Give an example of a relation which is reflexive and transitive but not symmetric?

Give an example of a relation which is symmetric and transitive but not reflexive?

Give an example of a relation which is symmetric but neither reflexive nor transitive?

Give an example of a relation which is transitive but neither reflexive nor symmetric?

Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, add a minimum number of ordered pairs so that the enlarged relation is symmeteric, transitive and reflexive.

Let A = {1, 2, 3} and R = {(1, 2), (1, 1), (2, 3)} be a relation on A. What minimum number of ordered pairs may be added to R so that it may become a transitive relation on A.

Let A = {a, b, c} and the relation R be defined on A as follows: R = {(a, a), (b, c), (a, b)}. Then, write minimum number of ordered pairs to be added in R to make it reflexive and transitive.

Defines a relation on N :
  x > y, x, y ∈  N

Determine the above relation is reflexive, symmetric and transitive.

Defines a relation on N :

x + y = 10, x, y∈ N

Determine the above relation is reflexive, symmetric and transitive.