NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.3
Chapter 1 Sets Exercise 1.3 NCERT Solutions for Class 11 Maths is very useful for finding the solutions of difficult questions. While solving Class 11 Maths NCERT Solutions then you can easily get accurate and step by step solutions from here. This will helpful in developing your skills so you could easily solve questions in the exams and obtain better marks.
1. Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:
(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 is a 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}.
Answer
Answer
(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 is a 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 same 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}
2. Examine whether the following statements are true or false:
(i) {a, b} ⊄ {b, c, a}
(ii) {a, e} ⊂ {x: x is a vowel in the English alphabet}
(iii) {1, 2, 3}⊂{1, 3, 5}
(iv) {a} ⊂{a, b, c}
(v) {a} ε {a, b, c}
(vi) {x: x is an even natural number less than 6} ⊂ {x: x is a natural number which divides 36}
Answer
Answer
(i) Since the element of the set {a, b} are also present in the set {b, c, a}, therefore {a, b} ⊂ {b, c, a} is false.
(ii) Vowels in the English alphabets are {a, e, i, o, u}.
{a, e} ⊂ {x: x is a vowel in the English alphabet} is true.
(iii) Since, all the elements of the set {1, 2, 3} are not present in the set {1, 3, 5}, therefore {1, 2, 3} ⊂ {1, 3, 5} is false.
(iv) Since, the element of the set {a} is present in the set {a, b, c}, therefore {a} Ì {a, b, c}is true.
(v) Since, a ε {a, b, c} is but not {a} ε {a, b, c}, therefore {a} ε {a, b, c} false.
(vi) {x: x is an even natural number less than 6}
= {2, 4} and {x: x is a natural number which divides 36}.
= {1, 2, 3, 4, 6, 9, 12, 18, 36}
Since, every element of the set {2, 4} is contained in the set {1, 2, 3, 4, 6, 9, 12, 18, 36} Hence, the given statement is true.
3. Let A = {1, 2 {3, 4}, 5}. Which of the following statements are incorrect and why?
(i) {3, 4} ⊂ A
(ii) {3, 4} ε A
(iii) {{3, 4}} ⊂ A
(iv) 1 ε A
(v) 1 ⊂ A
(vi) {1, 2, 5} ⊂ A
(vii) {1, 2, 5} ε A
(viii) {1, 2, 3} ⊂ A
(ix) Ф ε A
(x) Ф ⊂ A
(xi) {Ф} f ⊂ A
Answer
Answer
(i) Incorrect as {3, 4} is an element of the set A.
(ii) Correct as {3, 4} is an element of the set A.
(iii) Correct as {3, 4} is contained in the set A.
(iv) Correct as 1 is an element of the set A.
(v) Incorrect as 1 belongs to the set A, but not contained in A
(vi) Correct as all the elements of the set {1, 2, 5} are present in the set A.
(vii) Incorrect as {1, 2, 5} is not the element of the set A.
(viii) Incorrect as 3 is not an element of the set A.
(ix) Incorrect as Ф is not an element of the set A.
(x) Correct as empty set is a subset of every set.
(xi) Incorrect as {Ф} is not contained in the set A.
4. Write down all the subsets of the following sets:
4. Write down all the subsets of the following sets:
(i) {a}
(ii) {a, b}
(iii) {1, 2, 3}
(iv) Ф
Answer
(i) {a}, it has two possible subsets Ф, {a}.
(ii) {a, b}, it has four possible subsets Ф, {a}, {b}, {a, b}.
(iii) {1, 2, 3}, it has eight possible subsets: Ф, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}.
(iv) Ф, it has only one subset which is {Ф}.
5. How many elements has P(A), if A = Ф?
Answer
If A = Ф, then it has only one subset which is {Ф}. Hence, P(A) has only one element.
5. How many elements has P(A), if A = Ф?
Answer
If A = Ф, then it has only one subset which is {Ф}. Hence, P(A) has only one element.
6. Write the following as intervals:
(i) {x: x ε R, – 4 < x≤ 6}
(ii) {x: x ε R, – 12 < x < – 10}
(iii) {x: x ε R, 0 ≤ x < 7}
(iv) {x: x ε R, 3 ≤ x ≤ 4}
Answer
Answer
(i) (– 4, 6]
(ii) (–12, –10)
(iii) [0, 7)
(iv) [3, 4]
7. Write the following intervals in set-builder form:
7. Write the following intervals in set-builder form:
(i) (–3, 0)
(ii) [6, 12]
(iii) (6, 12]
(iv) [–23, 5)
Answer
(i) (–3, 0) = {x: x ε R, –3 < x < 0}
(ii) [6, 12] = {x, x ε R, 6 ≤ x ≤ 12}
(iii) (6, 12] = {x: x ε R, 6 < x ≤ 12}
(iv) [– 23, 5] = {x: x ε R, –23 ≤ x < 5}
8. What universal set(s) would you propose for each of the following:
Answer
(i) (–3, 0) = {x: x ε R, –3 < x < 0}
(ii) [6, 12] = {x, x ε R, 6 ≤ x ≤ 12}
(iii) (6, 12] = {x: x ε R, 6 < x ≤ 12}
(iv) [– 23, 5] = {x: x ε R, –23 ≤ x < 5}
8. What universal set(s) would you propose for each of the following:
(i) The set of right triangles.
(ii) The set of isosceles triangles.
Answer
Answer
(i) The set of triangles.
(ii) The set of triangles.
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 universal set (s) for all the three sets A, B and C.
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 universal set (s) for all the three sets A, B and C.
(i) {0, 1, 2, 3, 4, 5, 6}
(ii) {Ф}
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(iv) {1, 2, 3, 4, 5, 6, 7, 8}
Answer
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} may be considered as universal set for all the three sets A, B and C.
Answer
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} may be considered as universal set for all the three sets A, B and C.