PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?

1 ∈ A

Let A = { 1, 2, { 3, 4}, 5 }. The following statement is correct or incorrect and why?

1 ⊂ A

Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?

{1, 2, 5} ⊂ A

Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?

{1, 2, 5} ∈ A

Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?

{1, 2, 3} ⊂ A

Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?

Φ ∈ A

Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?

Φ ⊂ A

Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?

{Φ} ⊂ A

Write down all the subsets of the following set:

{a, b}

Write down all the subsets of the following set:

{1, 2, 3}

Write down all the subsets of the following set:

Φ

If the ordered pairs (x, −1) and (5, y) belong to the set {(a, b) : b = 2a − 3}, find the values of x and y. 

If a ∈ [−1, 2, 3, 4, 5] and b ∈ [0, 3, 6], write the set of all ordered pairs (a, b) such that a + b= 5.  

If a ∈ [2, 4, 6, 9] and b ∈ [4, 6, 18, 27], then form the set of all ordered pairs (a, b) such that a divides b and a < b.

Let A and B be two sets such that n(A) = 3 and n(B) = 2.
If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y, z are distinct elements.

State whether of  the statement is true or false. If the statement is false, re-write the given statement correctly:

 If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ B and y ∈ A.

A relation R is defined from a set A = [2, 3, 4, 5] to a set B = [3, 6, 7, 10] as follows:
(x, y) ∈ R ⇔ x is relatively prime to y
Express R as a set of ordered pairs and determine its domain and range.

Let A be the set of first five natural numbers and let R be a relation on A defined as follows:
(x, y) ∈ R ⇔ x ≤ y
Express R and R⁻¹ as sets of ordered pairs. Determine also (i) the domain of R⁻¹ (ii) the range of R.

Write the relation as the sets of ordered pairs:

(i) A relation R from the set [2, 3, 4, 5, 6] to the set [1, 2, 3] defined by x = 2y.

Write the relation as the sets of ordered pairs:

(ii) A relation R on the set [1, 2, 3, 4, 5, 6, 7] defined by (x, y) ∈ R ⇔ x is relatively prime to y.