Sign in

Mathematics · Textbook solutions

Sets

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 78 questions

  1. Write the following sets in roster form.
    Ex 1.1 Q1(i)
    Set of even natural numbers
  2. Ex 1.1 Q1(ii)
    Set of even prime numbers from 1 to 50
  3. Ex 1.1 Q1(iii)
    Set of negative integers
  4. Ex 1.1 Q1(iv)
    Seven basic sounds of a sargam (sur)
  5. Write the following symbolic statements in words.
    Ex 1.1 Q2(i)
    43∈Q\frac{4}{3} \in \mathbb{Q}
  6. Ex 1.1 Q2(ii)
    −2∉N-2 \notin \mathbb{N}
  7. Ex 1.1 Q2(iii)
    P={p∣p is an odd number}P = \{p \mid p \text{ is an odd number}\}
  8. Ex 1.1 Q3
    Write any two sets by listing method and by rule method.
  9. Write the following sets using listing method.
    Ex 1.1 Q4(i)
    All months in the indian solar year.
  10. Ex 1.1 Q4(ii)
    Letters in the word 'COMPLEMENT'.
  11. Ex 1.1 Q4(iii)
    Set of human sensory organs.
  12. Ex 1.1 Q4(iv)
    Set of prime numbers from 1 to 20.
  13. Ex 1.1 Q4(v)
    Names of continents of the world.
  14. Write the following sets using rule method.
    Ex 1.1 Q5(i)
    A={1,4,9,16,25,36,49,64,81,100}A = \{1, 4, 9, 16, 25, 36, 49, 64, 81, 100\}
  15. Ex 1.1 Q5(ii)
    B={6,12,18,24,30,36,42,48}B = \{6, 12, 18, 24, 30, 36, 42, 48\}
  16. Ex 1.1 Q5(iii)
    C={S,M,I,L,E}C = \{S, M, I, L, E\}
  17. Ex 1.1 Q5(iv)
    D={Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}D = \{\text{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}\}
  18. Ex 1.1 Q5(v)
    X={a,e,t}X = \{a, e, t\}
  1. Ex 1.2 Q1
    Decide which of the following are equal sets and which are not? Justify your answer. A={x∣3x−1=2}A = \{x \mid 3x - 1 = 2\} B={x∣x is a natural number but x is neither prime nor composite.}B = \{x \mid x \text{ is a natural number but } x \text{ is neither prime nor composite.}\} C={x∣x∈N, x<2}C = \{x \mid x \in \mathbb{N},\ x < 2\}
  2. Ex 1.2 Q2
    Decide whether set A and B are equal sets. Give reason for your answer. A = Even prime numbers B={x∣7x−1=13}B = \{x \mid 7x - 1 = 13\}
  3. Which of the following are empty sets? why?
    Ex 1.2 Q3(i)
    A={a∣a is a natural number smaller than zero.}A = \{a \mid a \text{ is a natural number smaller than zero.}\}
  4. Ex 1.2 Q3(ii)
    B={x∣x2=0}B = \{x \mid x^2 = 0\}
  5. Ex 1.2 Q3(iii)
    C={x∣5x−2=0, x∈N}C = \{x \mid 5x - 2 = 0,\ x \in \mathbb{N}\}
  6. Write with reasons, which of the following sets are finite or infinite.
    Ex 1.2 Q4(i)
    A={x∣x<10, x is a natural number}A = \{x \mid x < 10,\ x \text{ is a natural number}\}
  7. Ex 1.2 Q4(ii)
    B={y∣y<−1, y is an integer}B = \{y \mid y < -1,\ y \text{ is an integer}\}
  8. Ex 1.2 Q4(iii)
    C = Set of students of class 9 from your school.
  9. Ex 1.2 Q4(iv)
    Set of people from your village.
  10. Ex 1.2 Q4(v)
    Set of apparatus in laboratory
  11. Ex 1.2 Q4(vi)
    Set of whole numbers
  12. Ex 1.2 Q4(vii)
    Set of rational number
  1. If A={a,b,c,d,e}A=\{a, b, c, d, e\}, B={c,d,e,f}B=\{c, d, e, f\}, C={b,d}C=\{b, d\}, D={a,e}D=\{a, e\} then which of the following statements are true and which are false?
    Ex 1.3 Q1(i)
    C⊆BC \subseteq B
  2. Ex 1.3 Q1(ii)
    A⊆DA \subseteq D
  3. Ex 1.3 Q1(iii)
    D⊆BD \subseteq B
  4. Ex 1.3 Q1(iv)
    D⊆AD \subseteq A
  5. Ex 1.3 Q1(v)
    B⊆AB \subseteq A
  6. Ex 1.3 Q1(vi)
    C⊆AC \subseteq A
  7. Take the set of natural numbers from 1 to 20 as universal set and show set X and Y using Venn diagram.
    Ex 1.3 Q2(i)
    X={x∣x∈N, and 7<x<15}X=\{x \mid x \in \mathbb{N}, \text{ and } 7<x<15\}
  8. Ex 1.3 Q2(ii)
    Y={y∣y∈N,y is prime number from 1 to 20}Y=\{y \mid y \in \mathbb{N}, y \text{ is prime number from 1 to 20}\}
  9. U={1,2,3,7,8,9,10,11,12}U=\{1, 2, 3, 7, 8, 9, 10, 11, 12\}, P={1,3,7,10}P=\{1, 3, 7, 10\}.
    Ex 1.3 Q3(i)
    Show the sets UU, PP and P′P' by Venn diagram.
  10. Ex 1.3 Q3(ii)
    Verify (P′)′=P(P')'=P.
  11. Ex 1.3 Q4
    A={1,3,2,7}A=\{1, 3, 2, 7\} then write any three subsets of A.
  12. P is the set of all residents in Pune. M is the set of all residents in Madhya Pradesh. I is the set of all residents in Indore. B is the set of all residents in India. H is the set of all residents in Maharashtra.
    Ex 1.3 Q5(i)
    Write the subset relation between the sets.
  13. Ex 1.3 Q5(ii)
    Which set can be the universal set for above sets?
  14. (6*) Which set of numbers could be the universal set for the sets given below?
    Ex 1.3 Q6(i)
    A=A= set of multiples of 5, B=B= set of multiples of 7, C=C= set of multiples of 12.
  15. Ex 1.3 Q6(ii)
    P=P= set of integers which are multiples of 4. T=T= set of all even square numbers.
  16. Ex 1.3 Q7
    Let all the students of a class be a Universal set. Let set A be the students who secure 50% or more marks in Maths. Then write the complement of set A.
  1. Ex 1.4 Q1
    If n(A)=15n(A)=15, n(A∪B)=29n(A \cup B)=29, n(A∩B)=7n(A \cap B)=7 then n(B)=n(B)= ?
  2. Ex 1.4 Q2
    In a hostel there are 125 students, out of which 80 drink tea, 60 drink coffee and 20 drink tea and coffee both. Find the number of students who do not drink tea or coffee.
  3. Ex 1.4 Q3
    In a competitive exam 50 students passed in English. 60 students passed in Mathematics. 40 students passed in both the subjects. None of them fail in both the subjects. Find the number of students who passed at least in one of the subjects?
  4. Ex 1.4 Q4*
    A survey was conducted to know the hobby of 220 students of class IX. Out of which 130 students informed about their hobby as rock climbing and 180 students informed about their hobby as sky watching. There are 110 students who follow both the hobbies. Then how many students do not have any of the two hobbies? How many of them follow the hobby of rock climbing only? How many students follow the hobby of sky watching only?
  5. Observe the given Venn diagram and write the following sets. In the diagram (universal set U): the region belonging to set A only contains x,y,zx, y, z; the intersection A∩BA \cap B contains m,nm, n; the region belonging to set B only contains p,q,rp, q, r; and outside both circles (but inside U) are s,ts, t.
    Ex 1.4 Q5(i)
    Write set AA.
  6. Ex 1.4 Q5(ii)
    Write set BB.
  7. Ex 1.4 Q5(iii)
    Write set A∪BA \cup B.
  8. Ex 1.4 Q5(iv)
    Write the universal set UU.
  9. Ex 1.4 Q5(v)
    Write set A′A'.
  10. Ex 1.4 Q5(vi)
    Write set B′B'.
  11. Ex 1.4 Q5(vii)
    Write set (A∪B)′(A \cup B)'.
  1. Choose the correct alternative answer for each of the following questions.
    Prob Q1(i)
    If M={1,3,5}M=\{1, 3, 5\}, N={2,4,6}N=\{2, 4, 6\}, then M∩N=M \cap N= ?
    1. A.
      {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\}
    2. B.
      {1,3,5}\{1, 3, 5\}
    3. C.
      ∅\varnothing
    4. D.
      {2,4,6}\{2, 4, 6\}
  2. Prob Q1(ii)
    P={x∣xP=\{x \mid x is an odd natural number, 1<x≤5}1 < x \le 5\}. How to write this set in roster form?
    1. A.
      {1,3,5}\{1, 3, 5\}
    2. B.
      {1,2,3,4,5}\{1, 2, 3, 4, 5\}
    3. C.
      {1,3}\{1, 3\}
    4. D.
      {3,5}\{3, 5\}
  3. Prob Q1(iii)
    P={1,2,…,10}P=\{1, 2, \ldots, 10\}, What type of set P is?
    1. A.
      Null set
    2. B.
      Infinite set
    3. C.
      Finite set
    4. D.
      None of these
  4. Prob Q1(iv)
    M∪N={1,2,3,4,5,6}M \cup N=\{1, 2, 3, 4, 5, 6\} and M={1,2,4}M=\{1, 2, 4\} then which of the following represent set N?
    1. A.
      {1,2,3}\{1, 2, 3\}
    2. B.
      {3,4,5,6}\{3, 4, 5, 6\}
    3. C.
      {2,5,6}\{2, 5, 6\}
    4. D.
      {4,5,6}\{4, 5, 6\}
  5. Prob Q1(v)
    If P⊆MP \subseteq M, then which of the following set represent P∩(P∪M)P \cap (P \cup M) ?
    1. A.
      PP
    2. B.
      MM
    3. C.
      P∪MP \cup M
    4. D.
      P′∩MP' \cap M
  6. Prob Q1(vi)
    Which of the following sets are empty sets?
    1. A.
      set of intersecting points of parallel lines
    2. B.
      set of even prime numbers.
    3. C.
      Month of an english calendar having less than 30 days.
    4. D.
      P={x∣x∈I,−1<x<1}P=\{x \mid x \in I, -1 < x < 1\}
  7. Find the correct option for the given question.
    Prob Q2(i)
    Which of the following collections is a set?
    1. A.
      Colours of the rainbow
    2. B.
      Tall trees in the school campus
    3. C.
      Rich people in the village
    4. D.
      Easy examples in the book
  8. Prob Q2(ii)
    Which of the following set represent N∩WN \cap W?
    1. A.
      {1,2,3,…}\{1, 2, 3, \ldots\}
    2. B.
      {0,1,2,3,…}\{0, 1, 2, 3, \ldots\}
    3. C.
      {0}\{0\}
    4. D.
      { }\{\ \}
  9. Prob Q2(iii)
    P={x∣xP=\{x \mid x is a letter of the word 'indian'}\} then which one of the following is set P in listing form?
    1. A.
      {i,n,d}\{i, n, d\}
    2. B.
      {i,n,d,a}\{i, n, d, a\}
    3. C.
      {i,n,d,i,a}\{i, n, d, i, a\}
    4. D.
      {n,d,a}\{n, d, a\}
  10. Prob Q2(iv)
    If T={1,2,3,4,5}T=\{1, 2, 3, 4, 5\} and M={3,4,7,8}M=\{3, 4, 7, 8\} then T∪M=T \cup M= ?
    1. A.
      {1,2,3,4,5,7}\{1, 2, 3, 4, 5, 7\}
    2. B.
      {1,2,3,7,8}\{1, 2, 3, 7, 8\}
    3. C.
      {1,2,3,4,5,7,8}\{1, 2, 3, 4, 5, 7, 8\}
    4. D.
      {3,4}\{3, 4\}
  11. Prob Q3
    Out of 100 persons in a group, 72 persons speak English and 43 persons speak French. Each one out of 100 persons speak at least one language. Then how many speak only English? How many speak only French? How many of them speak English and French both?
  12. Prob Q4
    70 trees were planted by Parth and 90 trees were planted by Pradnya on the occasion of Tree Plantation Week. Out of these; 25 trees were planted by both of them together. How many trees were planted by Parth or Pradnya?
  13. Prob Q5
    If n(A)=20n(A)=20, n(B)=28n(B)=28 and n(A∪B)=36n(A \cup B)=36 then n(A∩B)=n(A \cap B)= ?
  14. Prob Q6
    In a class, 8 students out of 28 have only dog as their pet animal at home, 6 students have only cat as their pet animal. 10 students have dog and cat both, then how many students do not have a dog or cat as their pet animal at home?
  15. Represent the union of two sets by Venn diagram for each of the following.
    Prob Q7(i)
    A={3,4,5,7}A=\{3, 4, 5, 7\}, B={1,4,8}B=\{1, 4, 8\}
  16. Prob Q7(ii)
    P={a,b,c,e,f}P=\{a, b, c, e, f\}, Q={l,m,n,e,b}Q=\{l, m, n, e, b\}
  17. Prob Q7(iii)
    X={x∣xX=\{x \mid x is a prime number between 80 and 100}\}, Y={y∣yY=\{y \mid y is an odd number between 90 and 100}\}
  18. Prob Q8
    Write the subset relations between the following sets. X=X= set of all quadrilaterals, Y=Y= set of all rhombuses, S=S= set of all squares, T=T= set of all parallelograms, V=V= set of all rectangles.
  19. Prob Q9
    If M is any set, then write M∪∅M \cup \varnothing and M∩∅M \cap \varnothing.
  20. Prob Q10*
    Observe the Venn diagram and write the given sets UU, AA, BB, A∪BA \cup B and A∩BA \cap B. In the diagram (universal set U): the region belonging to set A only contains 2,3,72, 3, 7; the intersection A∩BA \cap B contains 1,51, 5; the region belonging to set B only contains 8,9,108, 9, 10; and outside both ovals (but inside U) are 4,11,134, 11, 13.
  21. Prob Q11
    If n(A)=7n(A)=7, n(B)=13n(B)=13, n(A∩B)=4n(A \cap B)=4, then n(A∪B)=n(A \cup B)= ?