SETS Class 6

 

Worksheet 1

 Sets

A. Fill in the Blanks

  1. A set is a well-defined collection of _______.
  2. The symbol used to represent a set is _______.
  3. A set with no elements is called a/an _______ set or the _______ set.
  4. The number of elements in a set is called the _______ of the set.
  5. If every element of set A is also an element of set B, then A is called a _______ of B.

B. True or False

  1. A set can contain duplicate elements.
  2. The set of vowels in the English alphabet is {a, e, i, o, u}.
  3. The symbol for an empty set is ∅ or {}.
  4. A set containing all possible elements is called a universal set.
  5. The set {2, 4, 6, 8, 10} is an example of a finite set.

C. Multiple Choice Questions (MCQs)

  1. Which of the following represents a well-defined set?
    a) The set of tall boys in the class
    b) The set of even numbers less than 10
    c) The set of beautiful flowers in a garden
    d) The set of good books

  2. What is the cardinality of the set {1, 3, 5, 7}?
    a) 3
    b) 4
    c) 5
    d) 7

  3. The symbol ∈ means:
    a) Belongs to
    b) Subset of
    c) Not a subset of
    d) Does not belong to

  4. Which of the following is an example of a null set?
    a) The set of all odd numbers divisible by 2
    b) The set of all prime numbers less than 10
    c) The set of all natural numbers greater than 0
    d) The set of all even numbers less than 20

  5. The universal set is represented by:
    a) U
    b) ∅
    c) A
    d) ∈

D. Write the Following Sets in Roster Form

  1. The set of vowels in the English alphabet.
  2. The set of even numbers between 1 and 10.
  3. The set of months of the year starting with the letter "J".
  4. The set of prime numbers less than 15.
  5. The set of single-digit natural numbers.

E. Write the Following Sets in Set Builder Form

  1. {2, 4, 6, 8, 10}
  2. {January, June, July}
  3. {5, 10, 15, 20}
  4. {x | x is a vowel in the English alphabet}
  5. {x | x is an even number less than 12}

F. Solve the Following Problems

  1. Find the union of the sets A = {1, 2, 3} and B = {3, 4, 5}.

  2. Find the intersection of the sets C = {a, b, c, d} and D = {b, d, f, g}.

  3. If P = {2, 4, 6, 8} and Q = {4, 8, 12, 16}, find:

    • (i) P∪QP \cup Q
    • (ii) P∩QP \cap Q

  4. Write the complement of the set X = {1, 2, 3, 4} if the universal set U = {1, 2, 3, 4, 5, 6}.

  5. List all subsets of the set E = {a, b}.

G. Application-Based Questions

  1. In a school, students are enrolled in sports as follows:

    • Football = {A, B, C, D, E}
    • Basketball = {C, D, F, G}
      Find:
    • (i) Students who play both sports
    • (ii) Students who play only football

  2. A survey was conducted among 50 students to know their preferences for tea and coffee. The results were:

    • 30 like tea
    • 25 like coffee
    • 10 like both tea and coffee
      Using a Venn diagram, find:
    • (i) The number of students who like only tea
    • (ii) The number of students who like neither tea nor coffee

 Worksheet 2

SETS

1. Fill in the blanks:

  1. A set is a well-defined collection of ____________.
  2. The set of all natural numbers less than 10 is ___________.
  3. The symbol used to denote "belongs to" is __________.
  4. A set with no elements is called the __________ set.
  5. The set of all vowels in the English alphabet is __________.

2. Match the following:

Column AColumn B
(a) A = {2, 4, 6, 8, 10}(i) A = {1, 2, 3, 4, 5}
(b) B = {apple, banana, cherry}(ii) B = {5, 10, 15, 20}
(c) C = {1, 2, 3, 4, 5}(iii) C = {apple, banana, cherry}
(d) D = {5, 10, 15, 20}(iv) D = {2, 4, 6, 8, 10}

3. Write the set for the following:

  1. The set of all odd numbers less than 15.
  2. The set of all months in a year that have 31 days.
  3. The set of primary colors.
  4. The set of even numbers between 10 and 20.

4. True or False:

  1. {3, 5, 7, 9} is a set of prime numbers.
  2. The set of all even numbers is a finite set.
  3. {1, 2, 3, 4, 5} and {5, 4, 3, 2, 1} are equal sets.
  4. The set of days of the week is an empty set.

5. Venn Diagram:

  • Draw a Venn Diagram to represent the following sets:
    • Set A = {1, 2, 3, 4, 5}
    • Set B = {4, 5, 6, 7}
    List the elements of the following:
    1. A ∩ B (Intersection of A and B)
    2. A ∪ B (Union of A and B)
    3. A - B (Difference of A and B)
    4. B - A (Difference of B and A)

6. Set Notation:

  1. Express the following in set-builder notation:
    • The set of all even numbers between 1 and 20.
  2. Express the following in roster form:
    • The set of all letters in the word "MATH".

7. Answer the following:

  1. If A = {x | x is a prime number less than 10} and B = {x | x is an even number greater than 0 and less than 10}, find A ∩ B.
  2. Write the set containing the common elements of the following two sets:
    • Set X = {2, 3, 5, 7, 11, 13}
    • Set Y = {5, 7, 11, 17}
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