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.

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

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