PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions

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.

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?