MCQs: Ch 02 Sets, Functions and Groups

High quality MCQs of Chapter 02 Sets, Functions and Groups of Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The answers are given at the end of the page.

MCQs

  1. A well defined collection of distinct objects is called
    1. Relation
    2. Sets
    3. Function
    4. None of these
  2. The objects in a set are called
    1. Numbers
    2. Terms
    3. Elements
    4. None of these
  3. A set can be describing in different no. of ways are
    1. One
    2. Two
    3. Three
    4. Four
  4. Sets are generally represented by
    1. Small letters
    2. Greek letters
    3. Capital letters
    4. None of these
  5. The members of different sets usually denoted by
    1. Capital letters
    2. Greek letters
    3. Small letters
    4. None of these
  6. The symbol used for membership of a set is
    1. $\forall$
    2. $\wedge$
    3. $<$
    4. $\in$
  7. If every element of a set $A$ is also element of set $B$, then
    1. $A\cap B=\phi$
    2. $A=B$
    3. $B\subseteq A$
    4. $A \subseteq B$
  8. Two sets $A$ and $B$ are equal iff
    1. $A-B \neq \phi$
    2. $A=B$
    3. $A \subseteq B$
    4. $B\subseteq A$
  9. If every element of a set $A$ is also as element of set $B$, then
    1. $A\cap B=A$
    2. $B \subseteq A$
    3. $A\cap B=\phi$
    4. None of these
  10. If $A\subseteq B$ and $B\subseteq A$, then
    1. $A=\phi$
    2. $A \cup B=A$
    3. $A \cap B=\phi$
    4. $A=B$
  11. A set having only one element is called
    1. Empty set
    2. Universal set
    3. Singleton set
    4. None of these
  12. An empty set having elements
    1. No element
    2. At least one
    3. More than one
    4. None of these
  13. An empty set is a subset of
    1. Only universal set
    2. Every set
    3. Both $A$ and $B$
    4. None of these
  14. If $A$ is a subset of $B$ then $A=B$, then we say that $A$ is an
    1. Proper subset of $B$
    2. Empty set
    3. Improper subset of $B$
    4. None of these
  15. If $A$ and $B$ are disjoint sets then $A \cup B$ equals
    1. $A$
    2. $B\cup A$
    3. $\phi$
    4. $B$
  16. The set of a given set $S$ denoted by $P(S)$ containing all the possible subsets of $S$ is called
    1. Universal set
    2. Super set
    3. Power set
    4. None of these
  17. If $S=\{\}$, then $P(S)=--------$
    1. Empty set
    2. $\{\phi \}$
    3. Containing more than one element
    4. None of these
  18. If $S=\{a\}$, then $P(S)=--------$
    1. $\{a\}$
    2. $\{\phi\}$
    3. $\{\phi, a\}$
    4. $\{\phi, \{a\}\}$
  19. $n(S)$ denotes
    1. Order of a set $S$
    2. No. of elements of set $S$
    3. No. of subsets of $S$
    4. None of these
  20. In general if $n(S)=m$, then $nP(S=------$
    1. $2^{m+1}$
    2. $2^{m-1}$
    3. $2^{m}$
    4. None of these
  21. Universal set is a
    1. Subset of every set
    2. Equivalent to every set
    3. Super set of every set
    4. None of these
  22. If $A$ and $B$ are overlapping sets then $A\cap B$ equal
    1. $A$
    2. $B$
    3. Non-empty
    4. None of these
  23. If $U$ is universal set and $A$ is proper subset of $U$ then the compliment of $A$ i.e. $A'$ is equals
    1. $\phi$
    2. $U$
    3. $U-A$
    4. None of these
  24. If $A$ and $B$ are disjoint sets then $n(A\cup B)=-----$
    1. $n(A)$
    2. $n(A)+n(B)$
    3. $n(B)$
    4. None of these
  25. If $A$ and $B$ are overlapping sets then $n(A\cup B)=-----$
    1. $n(A)+n(B)$
    2. $n(A)-n(B)$
    3. $n(A)+n(B)-n(A\cap B)$
    4. None of these
  26. If $A \subseteq B$ then $A \cup B=$——
    1. $A$
    2. $\phi$
    3. $A \cap B$
    4. $B$
  27. If $A \subseteq B$ then $A \cap B=$——
    1. $B$
    2. $A \cup$
    3. $\phi$
    4. $A$
  28. If $A$ and $B$ are overlapping sets then $n(A- B)=-----$
    1. $n(A)$
    2. $n(A)-n(A\cap B)$
    3. $n(A)-n(A\cup B)$
    4. $n(A)+n(A\cap B)$
  29. If $A$ and $B$ are disjoint sets then $n(B-A)=-----$
    1. $n(B)$
    2. $n(A)$
    3. $\phi$
    4. None of these
  30. If $A$ and $B$ are disjoint sets then $B-A=-----$
    1. $A$
    2. $B$
    3. $\phi$
    4. None of these
  31. If $A \subseteq B$ then $A-B=$——
    1. $n(B)$
    2. $n(A)$
    3. $\phi$
    4. None of these
  32. If $A \subseteq B$ then $n(A-B)=$——
    1. $n(A)$
    2. $n(B)$
    3. One
    4. Zero
  33. If $B \subseteq A$ then $A-B=$——
    1. $n(A)$
    2. $B$
    3. $\phi$
    4. non-empty
  34. If $B \subseteq A$ then $n(A-B)=$——
    1. $n(A)$
    2. $n(B)$
    3. $n(A)-n(B)$
    4. None of these
  35. If $A$ and $B$ are overlapping sets then $n(B-A)=-----$
    1. $n(B)$
    2. $n(A)$
    3. $\phi$
    4. non-empty
  36. If $A \subseteq B$ then $B-A=$——
    1. $B$
    2. $A$
    3. $\phi$
    4. None of these
  37. If $A \subseteq B$ then $n(B-A)=$——
    1. $n(B)$
    2. $n(A)$
    3. $n(B)-n(A)$
    4. $\phi$
  38. If $B \subseteq A$ then $B-A=$——
    1. $B$
    2. $A$
    3. $\phi$
    4. None of these
  39. If $B \subseteq A$ then $n(B-A)=$——
    1. $n(A)$
    2. $n(B)$
    3. One
    4. Zero
  40. For subsets $A$ and $B$, $A \cup(A' \cup B)=$——
    1. $A \cap B$
    2. $A$
    3. $A \cup B$
    4. None of these
  41. A declarative statement which may be true or false but not both is called a
    1. Induction
    2. Deduction
    3. Equation
    4. Proposition
  42. Deductive logic in which every statement is regarded as true or false and there is no other possibility is called
    1. Proposition
    2. Non-Aristotelian logic
    3. Aristotelian logic
    4. None of these
  43. If $p$ and $q$ are two statements then $p \vee q$ represents
    1. Conjunction
    2. Conditional
    3. Disjunction
    4. None of these
  44. If $p$ and $q$ are two statements then $p \wedge q$ represents
    1. Conjunction
    2. Disjunction
    3. Conditional
    4. None of these
  45. Logical expression $p \vee q$ is read as
    1. $p$ and $q$
    2. $p$ or $q$
    3. $p$ minus $q$
    4. None of these
  46. Logical expression $p \wedge q$ is read as
    1. $p \times q$
    2. $p$ or $q$
    3. $p$ minus $q$
    4. $p$ and $q$
  47. A compound statement of the form if $p$ and $q$ is called
    1. Hypothesis
    2. Conclusion
    3. Conditional
    4. None of these
  48. Statement $p \longrightarrow (q \longrightarrow r)$ is equivalent to
    1. $(p \vee q)\longrightarrow r$
    2. $(p \wedge q)\longrightarrow r$
    3. $p \longrightarrow (q \wedge r)$
    4. $(r \longrightarrow q)\longrightarrow p$
  49. A statement which is true for all possible values of the variables involved in it is called
    1. Absurdity
    2. Contingency
    3. Quantifier
    4. Tautology
  50. A statement which is always false is called
    1. Tautology
    2. Contingency
    3. Absurdity
    4. Quantifier
  51. A statement which can be true or false depending upon the truth values of the variable involved in it is called
    1. Absurdity
    2. Quantifier
    3. Tautology
    4. Contingency
  52. The words or symbols which convey the idea of quality or number are called
    1. Contingency
    2. Contradiction
    3. Quantifier
    4. None of these
  53. The symbol $\forall$ stand for
    1. There exist
    2. Belongs to
    3. Such that
    4. For all
  54. The symbol $\exists$ stand for
    1. Belongs to
    2. Such that
    3. For all
    4. There exists
  55. Truth set of tautology in the relevant universal set and that of an absurdity is the
    1. Empty set
    2. Difference set
    3. Universal set
    4. None of these
  56. Logical form of $(A \cup B)'$ is given by
    1. $p \vee q$
    2. $p \wedge q$
    3. $\sim (p \wedge q)$
    4. $\sim (p \vee q)$
  57. Logical form of $(A \cap B)'$ is given by
    1. $\sim (p \vee q)$
    2. $p \wedge q$
    3. $\sim (p \wedge q)$
    4. None of these
  58. Logical form of $A' \cap B'$ is given by
    1. $\sim p \wedge q$
    2. $p \wedge \sim q$
    3. $\sim p \vee \sim q$
    4. $\sim p \wedge \sim q$
  59. Logical form of $A' \cup B'$ is given by
    1. $p \vee q$
    2. $\sim p \vee q$
    3. $\sim p \vee \sim q$
    4. $\sim p \wedge \sim q$
  60. Every relation is
    1. Function
    2. Cartesian product
    3. May or may not be function
    4. None of these
  61. For two non-empty sets $A$ and $B$, the Cartesian product $A\times B$ is called
    1. Binary operation
    2. Binary relation
    3. Function
    4. None of these
  62. The set of the first elements of the ordered pairs forming a relation is called its
    1. Subset
    2. Domain
    3. Range
    4. None of these
  63. The set of the second elements of the ordered pairs forming a relation is called its
    1. Subset
    2. Complement
    3. Range
    4. None of these
  64. A function maybe
    1. Relation
    2. Subset of Cartesian product
    3. Both A and B
    4. None of these
  65. If a function $f: A \longrightarrow B$ is such that Ran$f \neq B$ then $f$ is called a function from
    1. $A$ onto $B$
    2. $A$ into $B$
    3. Both A and B
    4. None of these
  66. If a function $f: A \longrightarrow B$ is such that Ran$f = B$ then $f$ is called a function from
    1. $A$ into $B$
    2. Bijective function
    3. Onto
    4. None of these
  67. The function $\{(x,y)/y=mx+c\}$ is called a
    1. Linear function
    2. Quadratic function
    3. Both A and B
    4. None of these
  68. Graph of a linear function geometrically represents a
    1. Circle
    2. Straight line
    3. Parabola
    4. None of these
  69. The inverse of a function is
    1. A function
    2. May not be a function
    3. May or may not be a function
    4. None of these
  70. The inverse of the linear function is a
    1. Not linear function
    2. A linear function
    3. Relation
    4. None of these
  71. The negation of a given number is called
    1. Binary operation
    2. A function
    3. Unary operation
    4. A relation
  72. A $*$ binary operation is called commutative in $S$ if $\forall a, b \in S $
    1. $a * b=ab$
    2. $a * b=a * b$
    3. $a * b=ba$
    4. $a * b=b * a$
  73. A $a \in S \exists$ are element $a' \in S$ such that $a \times a'=a' \times a=e$ then $a'$
    1. Inverse of $a$
    2. not inverse of $a$
    3. Compliment
    4. None of these
  74. The set $\{1,w,w^2\}$, when $w^3=1$ is a
    1. Abelian group w.r.t. addition
    2. Semi group w.r.t. addition
    3. Group w.r.t. subtraction
    4. Abelian group w.r.t. multiplication
  75. Let $A$ and $B$ any non-empty sets, then $A\cup (A\cap B)$ is
    1. $B \cap A$
    2. $A$
    3. $A \cup B$
    4. $B$
  76. $A\cup B=A \cap B$ then $A$ is equal to
    1. $B$
    2. $\phi$
    3. $A$
    4. $B$
  77. Which of the following sets has only one subset
    1. $\{x,y\}$
    2. $\{x\}$
    3. $\{y\}$
    4. $\{\}$
  78. $A$ is subset of $B$ if
    1. Every element of $B \in A$
    2. Every element of $B \neq A$
    3. Every element of $A \in B$
    4. Some element of $B \in A$
  79. The complement of set $A$ relative to the universal set $\bigcup$ is the set
    1. $\{x/x \in \bigcup and x\in A\}$
    2. $\{x/x \neq \bigcup and x\in A\}$
    3. $\{x/x \neq \bigcup and x\neq A\}$
    4. $\{x/x \in \bigcup and x\neq A\}$
  80. If $\frac{A}{B}=A$ then
    1. $A\cap =\phi$
    2. $A\cap B =A$
    3. $A\cap B =B$
    4. $A\cap B =0$
  81. The property used in the equation $(x-y)z=xz-yz$ is
    1. Associative law
    2. Distributive law
    3. Commutative law
    4. Identity Law
  82. The property used in the equation $\sqrt{2}\times \sqrt{5}=\sqrt{5}\times \sqrt{2}$ is
    1. Identity
    2. Commutative law for multiplication
    3. Closure law
    4. Commutative addition
  83. If $A$, $B$ are any sets, then $A- B=?$
    1. $A-(A \cap B)$
    2. $A\cap(A -B)$
    3. $A'-(A \cap B)$
    4. $A-(A' \cap B)$
  84. If $A$ is a non-empty set then binary operation is
    1. Subset $A\times A$
    2. A function $A\times A$ into $A$
    3. Not a function $A\times A$ into $A$
    4. A function $A$ into $A$
  85. Let $A$ and $B$ are two sets and $A\subseteq U$ and $B\subseteq U$ then $U$ is said to be
    1. Empty set
    2. Power set
    3. Proper set
    4. Universal set
  86. The identity element with respect to subtraction is
    1. $0$
    2. $-1$
    3. $1$
    4. $0$ and $1$
  87. Let $X$ has three elements then $P(X)$ has elements
    1. $3$
    2. $4$
    3. $8$
    4. $12$
  88. Every set is a —— subset of itself.
    1. Proper
    2. Improper
    3. Finite
    4. None of these
  89. If $A$ and $B$ are disjoint sets, then shaded region represents
    1. $A^c \cup B^c$
    2. $A^c \cap B^c$
    3. $A \cup B$
    4. $A-B$
  90. Conditional and its contrapositive are ———-
    1. Equivalent
    2. Equal
    3. Inverse
    4. None of these
  91. A statement which is already false is called an ———
    1. Absurdity
    2. Contrapositive
    3. Bi-conditional
    4. None of these
  92. The graph of a quadratic function is ———
    1. Straight line
    2. Parabola
    3. Linear function
    4. Onto function
  93. If $A$ is non-empty set, then any subset of $A \times A$ is called ——— on $A$
    1. Domain
    2. Range
    3. Relation
    4. None of these
  94. The unary operation is an operation which yield another number when performed on ———
    1. Two numbers
    2. A single number
    3. Three numbers
    4. All of these
  95. The constant function is ——-
    1. $y=k$
    2. $y=f(x)$
    3. $x=f(y)$
    4. None of these
  96. Binary operation means an operation which require ———
    1. One element
    2. Two elements
    3. Three elements
    4. All of these
  97. A group is said to be ——– if it contains finite numbers of elements
    1. Finite group
    2. Semi group
    3. Monoid
    4. Groupoid
  98. $Z$ is a group under ——
    1. Subtraction
    2. Division
    3. Multiplication
    4. Addition
  99. $\{3n, n \in z\}$ is an ablian group under ——
    1. Addition
    2. Subtraction
    3. Division
    4. None of these
  100. A semi group is always a —–
    1. Group
    2. Groupoid
    3. Monoid
    4. Addition
  101. The one-one function is —–
    1. Straight line
    2. Circle
    3. Parabola
    4. Ellipse

Answers

1-b, 2-c, 3-c, 4-c, 5-d, 6-a, 7-d, 8-b, 9-a, 10-d, 11-a, 12-a, 13-b, 14-c, 15-b, 16-c, 17-b, 18-d, 19-b, 20-c, 21-c, 22-c, 23-c, 24-b, 25-c, 26-d, 27-d, 28-b, 29-a, 30-b, 31-c, 32-d, 33-d, 34-c, 35-d, 36-d, 37-c, 38-c, 39-c, 40-c, 41-d, 42-d, 43-c, 44-a, 45-b, 46-d, 47-c, 48-b, 49-d, 50-c, 51-d, 52-c, 53-d, 54-d, 55-a, 56-c, 57-a, 58-d, 59-d, 60-c, 61-b, 62-b, 63-c, 64-c, 65-b, 66-c, 67-a, 68-b, 69-c, 70-b, 71-c, 72-d, 73-a, 74-d, 75-b, 76-a, 77-d, 78-a, 79-d, 80-a, 81-b, 82-b, 83-a, 84-b, 85-b, 86-a, 87-c, 88-b, 89-a, 90-a, 91-a, 92-b, 93-c, 94-b, 95-d, 96-b, 97-a, 98-d, 99-a, 100-b, 101-d

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