11th NCERT Sets Exercise 1.3 Questions 9

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Question (1)

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:

Solution

(i) {2, 3, 4}   ⊂   {1, 2, 3, 4, 5}.
(ii) {a, b, c}   ⊄  {b, c, d}
(iii) {x: x is a student of Class XI of your school}   ⊂   {x: x student of your school}
(iv) {x: x is a circle in the plane}   ⊄ {x: x is a circle in the same plane with radius 1 unit}
(v) {x: x is a triangle in a plane}   ⊄   {x: x is a rectangle in the plane}
(vi) {x: x is an equilateral triangle in a plane}   ⊂   {x: x is a triangle in the same plane}
(vii) {x: x is an even natural number}   ⊂   {x: x is an integer}

Question (2)

Examine whether the following statements are true or false:
(i) {a, b} ⊄ {b, c, a}

Solution

{ a, b} is the subset of { a, b, c} So statement is false.
(ii) {a, e} ⊂ {x: x is a vowel in the English alphabet}

Solution

The statement is true.
(iii) {1, 2, 3} ⊂{1, 3, 5}

Solution

The statement is false.
(iv) {a} ⊂ {a. b, c}

Solution

Yes it is a subset, The statement is true.
(v) {a} ∈ (a, b, c)

Solution

Set never belongs to other set. The statement is false.
(vi) {x: x is an even natural number less than 6} ⊂ {x: x is a natural number which divides 36}

Solution

A = { 2, 4 } , B = { 1, 2, 3, 4, 6, 9, 12, 18, 36}
A is subset of B . The statement is true.

Question (3)

Let A= {1, 2, {3, 4,}, 5}. Which of the following statements are incorrect and why?
(i) {3, 4}⊂ A

Solution

{3, 4 } is an element of A . it is not subset. The statement is not correct.
(ii) {3, 4}}∈ A

Solution

{3, 4} is an element of set A. The statement is correct.
(iii) {{3, 4}}⊂ A

Solution

As it is subset of A. The statement is true.
(iv) 1∈ A

Solution

The statement is correct.
(v) 1⊂ A

Solution

for subset it must be set first. The statement is not correct.
(vi) {1, 2, 5} ⊂ A

Solution

It is sub set of A . The statement is correct.
(vii) {1, 2, 5} ∈ A

Solution

Set is never belongs to A. The statement is not correct.
(viii) {1, 2, 3} ⊂ A

Solution

3 is not the element of set A. The set is not subset. The statement is not correct.
(ix) Φ ∈ A

Solution

It is null set. set is not element of the other set. The statement is nor correct.
(x) Φ ⊂ A

Solution

The null set is subset of each and every set. The statement is correct.
(xi) {Φ} ⊂ A

Solution

Ø is not the elemnt of set A. The statement is not correct.

Question (4)

Write down all the subsets of the following sets:
(i) {a}

Solution

All possible sub sets are { }, {a} .
(ii) {a, b}

Solution

It will have 4 subsets. they are { }, {a}, {b}, {a, b}.
(iii) {1, 2, 3}

Solution

It will have 8 subsets.
they are { }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}.
(iv) Φ

Solution

The null set is only one subset.

Question (5)

How many elements has P(A), if A = Φ?

Solution

If A is null set it does not have any elements.
P(A) is powerset of A. It is set of all possible subset of a set A.
The null set is the sub set of null set. P(A) will have 1 element.

Question (6)

Write the following as intervals:
(i) {x: x ∈ R, –4 < x ≤ 6}

Solution

The interval form is ( - 4 ,6] (ii) {x: x ∈ R, –12 < x < –10}

Solution

The interval form is ( -12, -10)
(iii) {x: x ∈ R, 0 ≤ x < 7}

Solution

The interval form is [ 0, 7 ) .
(iv) {x: x ∈ R, 3 ≤ x ≤ 4}

Solution

The interval form is [ 3, 4 }

Question (7)

Write the following intervals in set-builder form:
(i) (–3, 0)

Solution

The set builder form is { x : x ∈ R , -3 < x < 0 }
(ii) [6, 12]

Solution

The set builder form is { x : x ∈ R , 6 ≤ x ≤ 12 }
(iii) (6, 12]

Solution

The set builder form is { x : x ∈ R ,6 < x ≤12 }
(iv) [–23, 5)

Solution

The set builder form is { x : x ∈ R , -23 ≤ x <5 }

Question (8)

What universal set (s) would you propose for each of the following:
(i) The set of right triangles

Solution

The set of all triangles in the plane.
(ii) The set of isosceles triangles

Solution

The set of all triangles in a plane.

Question (9)

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universals set (s) for all the three sets A, B and C
(i) {0, 1, 2, 3, 4, 5, 6}

Solution

All elements of set A and B are present but all elements of C is not present in it. It will be not universal set for sets A, B and C.
(ii) Φ

Solution

it is null set does not have any element.
It can not be universal set for set A and B and C.
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Solution

In this set all elements of set A, B and C are present. So it is universal set for set A, B and C.
(iv) {1, 2, 3, 4, 5, 6, 7, 8}

Solution

The element '0' of set C is not present in this set. So it is not the universal set for set A, B and C.