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Federal (FBISE) · Chapter test · Free

9th Class Mathematics Chapter 3 Test03. Sets and Relations

30 marks · 40 minutes · 21 questions. Covers: 03. Sets and Relations.

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9th Class Mathematics Chapter 3 Test

9th Class · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 30Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

  1. For three sets, the central region of a Venn diagram represents:
    1. A ∪ B ∪ C
    2. A ∩ B ∩ C
    3. A − B
    4. A′
  2. An ordered pair is written as:
    1. {a, b}
    2. (a, b)
    3. [a, b]
    4. a + b
  3. The Venn diagram is used to represent:
    1. Numbers only
    2. Relations between sets
    3. Equations only
    4. Angles
  4. If 52 people speak Arabic and 112 speak French, those who speak both are represented by:
    1. A ∪ F
    2. A ∩ F
    3. A − F
    4. F′
  5. The set containing all elements of A and B is called:
    1. Intersection
    2. Union
    3. Difference
    4. Complement
  6. In the ordered pair (a, b), a is called the:
    1. Second element
    2. First element
    3. Range
    4. Relation
  7. If n(A) = 23, n(A ∪ B) = 44 and n(A ∩ B) = 2, then n(B) is:
    1. 19
    2. 21
    3. 23
    4. 25
  8. If R = {(1,2),(2,3)}, then R⁻¹ is:
    1. {(1,2),(2,3)}
    2. {(2,1),(3,2)}
    3. {(1,3),(2,2)}
    4. {(3,1),(2,2)}
  9. A − B contains elements which are:
    1. In both A and B
    2. In A but not in B
    3. In B but not in A
    4. Outside both sets
  10. If (2,5) ∈ R, then in R⁻¹ we have:
    1. (2,5)
    2. (5,2)
    3. (−2,−5)
    4. (5,5)

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. Given that D = {a, e, i}, E = {a, c}, F = {b, c}. Find D×(E∩F)D \times (E \cap F )
  2. If A = Set of Natural numbers and R={(x,y)∣x∈A∧y∈A} i.e. R⊆A×A. R = \{(x, y) \mid x \in A \land y \in A\} \text{ i.e. } R \subseteq A \times A. . Then find the domain and range of R.
  3. Find all possible binary relations in the case mentioning the number of binary relation in case.C = {π , e}
  4. Let E = {1, 3} and F = {4, 6, 8}. Express by graphically.E × E
  5. Exhibit P×Q P \times Q by arrow diagram when P = { a , b , c } , Q = { d , e }
  6. Shade A∩(B∪C) A \cap (B \cup C) in the following Venn diagram.Question diagram
  7. Defne binary relation.
  8. If A = { 5 , 10 , 15 , 20 , 25 } Find the number of binary relations in A.

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  1. Prove by using Venn diagram when P = {0, 1, 2, 3} , Q = {2, 3, 4, 5, 6} and R = { 5, 6, 7, 8, 9} (P∪Q)∪R=P∪(Q∪R)(P \cup Q) \cup R = P \cup (Q \cup R)
  2. ABC Dairy polls its customers on their favorite flavor: chocolate, vanilla or mango? 100 customers said they like mango flavor, 90 customers said they like vanilla, 40 polled for chocolate, 20 customers liked both mango and vanilla while 14 liked both chocolate and vanilla. How many customers said they like: (1) only mango? (2) only vanilla (3) only chocolate
  3. In a survey of 60 people, it was found that 25 people watch channel A, 16 watch channel B, 13 watch channel C, 4 watch both A and B, 7 watch both B and C, 8 watch both A and C, watch all three channels. Find the number of people who watch at least one of the channels? Also find the number of people who do not watch these channels.