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

Define an equivalence relation ?

If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by "is less than", write R as a set ordered pairs.

A = {1, 2, 3, 4, 5, 6, 7, 8} and if R = {(x, y) : y is one half of x; x, y ∈ A} is a relation on A, then write R as a set of ordered pairs.

Let A = {2, 3, 4, 5} and B = {1, 3, 4}. If R is the relation from A to B given by a R b if "a is a divisor of b". Write R as a set of ordered pairs.

Evaluate the following:

`sin(cos^-1  5/13)`

State the reason for the relation R on the set {1, 2, 3} given by R = {(1, 2), (2, 1)} to be transitive ?

Let R = {(a, a³) : a is a prime number less than 5} be a relation. Find the range of R.

Let R be the equivalence relation on the set Z of the integers given by R = { (a, b) : 2 divides a - b }.

Write the equivalence class [0].

For the set A = {1, 2, 3}, define a relation R on the set A as follows:
R = {(1, 1), (2, 2), (3, 3), (1, 3)}
Write the ordered pairs to be added to R to make the smallest equivalence relation.

Let A = {0, 1, 2, 3} and R be a relation on A defined as
R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}
Is R reflexive? symmetric? transitive?

Evaluate the following:

`sin(tan^-1  24/7)`

Let the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b) : | a²- b² | < 8}. Write R as a set of ordered pairs.

Let the relation R be defined on N by aRb iff 2a + 3b = 30. Then write R as a set of ordered pairs

Write the smallest equivalence relation on the set A = {1, 2, 3} ?

Let R be a relation on the set N given by
R = {(a, b) : a = b − 2, b > 6}. Then,

Evaluate the following:

`sin(sec^-1  17/8)`

If a relation R is defined on the set Z of integers as follows:
(a, b) ∈ R ⇔ a² + b² = 25. Then, domain (R) is ___________

R is a relation on the set Z of integers and it is given by
(x, y) ∈ R ⇔ | x − y | ≤ 1. Then, R is ______________ .

The relation R defined on the set A = {1, 2, 3, 4, 5} by
R = {(a, b) : | a² − b² | < 16} is given by ______________ .

Evaluate the following:

`cosec(cos^-1  3/5)`