PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

{1, 2, 3} ⊂ {1, 3, 5}

{a} ⊂ {a. b, c}

{a} ∈ (a, b, c)

{x : x is an even natural number less than 6} ⊂ {x : x is a natural number which divides 36}

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

{3, 4} ⊂ A

Write down all the subsets of the following set:

{a}

How many elements has P(A), if A = Φ?

Write the following as interval:

{x : x ∈ R, – 4 < x ≤ 6}

Write the following as intervals:  {x: x ∈ R, –12 < x < –10}

Write the following as intervals: {x : x ∈ R, 0 ≤ x < 7}

Write the following as intervals: {x : x ∈ R, 3 ≤ x ≤ 4}

Write the given intervals in set-builder form:

(–3, 0)

Write the given intervals in set-builder form:

[6, 12]

Write the following interval in set-builder form:

(6, 12]

Write the following interval in set-builder form:

[–23, 5)

Decide, among the following sets, which sets are subsets of one and another:

A = {x : x ∈ R and x satisfy x² – 8x + 12 = 0},

B = {2, 4, 6}, C = {2, 4, 6, 8, …}, D = {6}.

Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If x ∈ A and A ∈ B, then x ∈ B

Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If A ⊂ B and B ∈ C, then A ∈ C

Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If A ⊂ B and B ⊂ C, then A ⊂ C

Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If A ⊄ B and B ⊄ C, then A ⊄ C