Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

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.

Evaluate the following:

`sec^-1(sec  pi/3)`

Evaluate the following:

`sec^-1(sec  (2pi)/3)`

Evaluate the following:

`sec^-1(sec  (5pi)/4)`

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.

Evaluate the following:

`sec^-1(sec  (7pi)/3)`

Evaluate the following:

`sec^-1(sec  (9pi)/5)`

Evaluate the following:

`sec^-1{sec  (-(7pi)/3)}`

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?

Evaluate the following:

`sec^-1(sec  (13pi)/4)`

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

Evaluate the following:

`sec^-1(sec  (25pi)/6)`

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.