# 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

- A well defined collection of distinct objects is called
- Relation
- Sets
- Function
- None of these

- The objects in a set are called
- Numbers
- Terms
- Elements
- None of these

- A set can be describing in different no. of ways are
- One
- Two
- Three
- Four

- Sets are generally represented by
- Small letters
- Greek letters
- Capital letters
- None of these

- The members of different sets usually denoted by
- Capital letters
- Greek letters
- Small letters
- None of these

- The symbol used for membership of a set is
- $\forall$
- $\wedge$
- $<$
- $\in$

- If every element of a set $A$ is also element of set $B$, then
- $A\cap B=\phi$
- $A=B$
- $B\subseteq A$
- $A \subseteq B$

- Two sets $A$ and $B$ are equal iff
- $A-B \neq \phi$
- $A=B$
- $A \subseteq B$
- $B\subseteq A$

- If every element of a set $A$ is also as element of set $B$, then
- $A\cap B=A$
- $B \subseteq A$
- $A\cap B=\phi$
- None of these

- If $A\subseteq B$ and $B\subseteq A$, then
- $A=\phi$
- $A \cup B=A$
- $A \cap B=\phi$
- $A=B$

- A set having only one element is called
- Empty set
- Universal set
- Singleton set
- None of these

- An empty set having elements
- No element
- At least one
- More than one
- None of these

- An empty set is a subset of
- Only universal set
- Every set
- Both $A$ and $B$
- None of these

- If $A$ is a subset of $B$ then $A=B$, then we say that $A$ is an
- Proper subset of $B$
- Empty set
- Improper subset of $B$
- None of these

- If $A$ and $B$ are disjoint sets then $A \cup B$ equals
- $A$
- $B\cup A$
- $\phi$
- $B$

- The set of a given set $S$ denoted by $P(S)$ containing all the possible subsets of $S$ is called
- Universal set
- Super set
- Power set
- None of these

- If $S=\{\}$, then $P(S)=--------$
- Empty set
- $\{\phi \}$
- Containing more than one element
- None of these

- If $S=\{a\}$, then $P(S)=--------$
- $\{a\}$
- $\{\phi\}$
- $\{\phi, a\}$
- $\{\phi, \{a\}\}$

- $n(S)$ denotes
- Order of a set $S$
- No. of elements of set $S$
- No. of subsets of $S$
- None of these

- In general if $n(S)=m$, then $nP(S=------$
- $2^{m+1}$
- $2^{m-1}$
- $2^{m}$
- None of these

- Universal set is a
- Subset of every set
- Equivalent to every set
- Super set of every set
- None of these

- If $A$ and $B$ are overlapping sets then $A\cap B$ equal
- $A$
- $B$
- Non-empty
- None of these

- If $U$ is universal set and $A$ is proper subset of $U$ then the compliment of $A$ i.e. $A'$ is equals
- $\phi$
- $U$
- $U-A$
- None of these

- If $A$ and $B$ are disjoint sets then $n(A\cup B)=-----$
- $n(A)$
- $n(A)+n(B)$
- $n(B)$
- None of these

- If $A$ and $B$ are overlapping sets then $n(A\cup B)=-----$
- $n(A)+n(B)$
- $n(A)-n(B)$
- $n(A)+n(B)-n(A\cap B)$
- None of these

- If $A \subseteq B$ then $A \cup B=$——
- $A$
- $\phi$
- $A \cap B$
- $B$

- If $A \subseteq B$ then $A \cap B=$——
- $B$
- $A \cup$
- $\phi$
- $A$

- If $A$ and $B$ are overlapping sets then $n(A- B)=-----$
- $n(A)$
- $n(A)-n(A\cap B)$
- $n(A)-n(A\cup B)$
- $n(A)+n(A\cap B)$

- If $A$ and $B$ are disjoint sets then $n(B-A)=-----$
- $n(B)$
- $n(A)$
- $\phi$
- None of these

- If $A$ and $B$ are disjoint sets then $B-A=-----$
- $A$
- $B$
- $\phi$
- None of these

- If $A \subseteq B$ then $A-B=$——
- $n(B)$
- $n(A)$
- $\phi$
- None of these

- If $A \subseteq B$ then $n(A-B)=$——
- $n(A)$
- $n(B)$
- One
- Zero

- If $B \subseteq A$ then $A-B=$——
- $n(A)$
- $B$
- $\phi$
- non-empty

- If $B \subseteq A$ then $n(A-B)=$——
- $n(A)$
- $n(B)$
- $n(A)-n(B)$
- None of these

- If $A$ and $B$ are overlapping sets then $n(B-A)=-----$
- $n(B)$
- $n(A)$
- $\phi$
- non-empty

- If $A \subseteq B$ then $B-A=$——
- $B$
- $A$
- $\phi$
- None of these

- If $A \subseteq B$ then $n(B-A)=$——
- $n(B)$
- $n(A)$
- $n(B)-n(A)$
- $\phi$

- If $B \subseteq A$ then $B-A=$——
- $B$
- $A$
- $\phi$
- None of these

- If $B \subseteq A$ then $n(B-A)=$——
- $n(A)$
- $n(B)$
- One
- Zero

- For subsets $A$ and $B$, $A \cup(A' \cup B)=$——
- $A \cap B$
- $A$
- $A \cup B$
- None of these

- A declarative statement which may be true or false but not both is called a
- Induction
- Deduction
- Equation
- Proposition

- Deductive logic in which every statement is regarded as true or false and there is no other possibility is called
- Proposition
- Non-Aristotelian logic
- Aristotelian logic
- None of these

- If $p$ and $q$ are two statements then $p \vee q$ represents
- Conjunction
- Conditional
- Disjunction
- None of these

- If $p$ and $q$ are two statements then $p \wedge q$ represents
- Conjunction
- Disjunction
- Conditional
- None of these

- Logical expression $p \vee q$ is read as
- $p$ and $q$
- $p$ or $q$
- $p$ minus $q$
- None of these

- Logical expression $p \wedge q$ is read as
- $p \times q$
- $p$ or $q$
- $p$ minus $q$
- $p$ and $q$

- A compound statement of the form if $p$ and $q$ is called
- Hypothesis
- Conclusion
- Conditional
- None of these

- Statement $p \longrightarrow (q \longrightarrow r)$ is equivalent to
- $(p \vee q)\longrightarrow r$
- $(p \wedge q)\longrightarrow r$
- $p \longrightarrow (q \wedge r)$
- $(r \longrightarrow q)\longrightarrow p$

- A statement which is true for all possible values of the variables involved in it is called
- Absurdity
- Contingency
- Quantifier
- Tautology

- A statement which is always false is called
- Tautology
- Contingency
- Absurdity
- Quantifier

- A statement which can be true or false depending upon the truth values of the variable involved in it is called
- Absurdity
- Quantifier
- Tautology
- Contingency

- The words or symbols which convey the idea of quality or number are called
- Contingency
- Contradiction
- Quantifier
- None of these

- The symbol $\forall$ stand for
- There exist
- Belongs to
- Such that
- For all

- The symbol $\exists$ stand for
- Belongs to
- Such that
- For all
- There exists

- Truth set of tautology in the relevant universal set and that of an absurdity is the
- Empty set
- Difference set
- Universal set
- None of these

- Logical form of $(A \cup B)'$ is given by
- $p \vee q$
- $p \wedge q$
- $\sim (p \wedge q)$
- $\sim (p \vee q)$

- Logical form of $(A \cap B)'$ is given by
- $\sim (p \vee q)$
- $p \wedge q$
- $\sim (p \wedge q)$
- None of these

- Logical form of $A' \cap B'$ is given by
- $\sim p \wedge q$
- $p \wedge \sim q$
- $\sim p \vee \sim q$
- $\sim p \wedge \sim q$

- Logical form of $A' \cup B'$ is given by
- $p \vee q$
- $\sim p \vee q$
- $\sim p \vee \sim q$
- $\sim p \wedge \sim q$

- Every relation is
- Function
- Cartesian product
- May or may not be function
- None of these

- For two non-empty sets $A$ and $B$, the Cartesian product $A\times B$ is called
- Binary operation
- Binary relation
- Function
- None of these

- The set of the first elements of the ordered pairs forming a relation is called its
- Subset
- Domain
- Range
- None of these

- The set of the second elements of the ordered pairs forming a relation is called its
- Subset
- Complement
- Range
- None of these

- A function maybe
- Relation
- Subset of Cartesian product
- Both A and B
- None of these

- If a function $f: A \longrightarrow B$ is such that Ran$f \neq B$ then $f$ is called a function from
- $A$ onto $B$
- $A$ into $B$
- Both A and B
- None of these

- If a function $f: A \longrightarrow B$ is such that Ran$f = B$ then $f$ is called a function from
- $A$ into $B$
- Bijective function
- Onto
- None of these

- The function $\{(x,y)/y=mx+c\}$ is called a
- Linear function
- Quadratic function
- Both A and B
- None of these

- Graph of a linear function geometrically represents a
- Circle
- Straight line
- Parabola
- None of these

- The inverse of a function is
- A function
- May not be a function
- May or may not be a function
- None of these

- The inverse of the linear function is a
- Not linear function
- A linear function
- Relation
- None of these

- The negation of a given number is called
- Binary operation
- A function
- Unary operation
- A relation

- A $*$ binary operation is called commutative in $S$ if $\forall a, b \in S $
- $a * b=ab$
- $a * b=a * b$
- $a * b=ba$
- $a * b=b * a$

- A $a \in S \exists$ are element $a' \in S$ such that $a \times a'=a' \times a=e$ then $a'$
- Inverse of $a$
- not inverse of $a$
- Compliment
- None of these

- The set $\{1,w,w^2\}$, when $w^3=1$ is a
- Abelian group w.r.t. addition
- Semi group w.r.t. addition
- Group w.r.t. subtraction
- Abelian group w.r.t. multiplication

- Let $A$ and $B$ any non-empty sets, then $A\cup (A\cap B)$ is
- $B \cap A$
- $A$
- $A \cup B$
- $B$

- $A\cup B=A \cap B$ then $A$ is equal to
- $B$
- $\phi$
- $A$
- $B$

- Which of the following sets has only one subset
- $\{x,y\}$
- $\{x\}$
- $\{y\}$
- $\{\}$

- $A$ is subset of $B$ if
- Every element of $B \in A$
- Every element of $B \neq A$

- Every element of $A \in B$
- Some element of $B \in A$

- The complement of set $A$ relative to the universal set $\bigcup$ is the set
- $\{x/x \in \bigcup and x\in A\}$
- $\{x/x \neq \bigcup and x\in A\}$

- $\{x/x \neq \bigcup and x\neq A\}$
- $\{x/x \in \bigcup and x\neq A\}$

- If $\frac{A}{B}=A$ then
- $A\cap =\phi$
- $A\cap B =A$
- $A\cap B =B$
- $A\cap B =0$

- The property used in the equation $(x-y)z=xz-yz$ is
- Associative law
- Distributive law
- Commutative law
- Identity Law

- The property used in the equation $\sqrt{2}\times \sqrt{5}=\sqrt{5}\times \sqrt{2}$ is
- Identity
- Commutative law for multiplication
- Closure law
- Commutative addition

- If $A$, $B$ are any sets, then $A- B=?$
- $A-(A \cap B)$
- $A\cap(A -B)$
- $A'-(A \cap B)$
- $A-(A' \cap B)$

- If $A$ is a non-empty set then binary operation is
- Subset $A\times A$
- A function $A\times A$ into $A$
- Not a function $A\times A$ into $A$
- A function $A$ into $A$

- Let $A$ and $B$ are two sets and $A\subseteq U$ and $B\subseteq U$ then $U$ is said to be
- Empty set
- Power set
- Proper set
- Universal set

- The identity element with respect to subtraction is
- $0$
- $-1$
- $1$
- $0$ and $1$

- Let $X$ has three elements then $P(X)$ has elements
- $3$
- $4$
- $8$
- $12$

- Every set is a —— subset of itself.
- Proper
- Improper
- Finite
- None of these

- If $A$ and $B$ are disjoint sets, then shaded region represents
- $A^c \cup B^c$
- $A^c \cap B^c$
- $A \cup B$
- $A-B$

- Conditional and its contrapositive are ———-
- Equivalent
- Equal
- Inverse
- None of these

- A statement which is already false is called an ———
- Absurdity
- Contrapositive
- Bi-conditional
- None of these

- The graph of a quadratic function is ———
- Straight line
- Parabola
- Linear function
- Onto function

- If $A$ is non-empty set, then any subset of $A \times A$ is called ——— on $A$
- Domain
- Range
- Relation
- None of these

- The unary operation is an operation which yield another number when performed on ———
- Two numbers
- A single number
- Three numbers
- All of these

- The constant function is ——-
- $y=k$
- $y=f(x)$
- $x=f(y)$
- None of these

- Binary operation means an operation which require ———
- One element
- Two elements
- Three elements
- All of these

- A group is said to be ——– if it contains finite numbers of elements
- Finite group
- Semi group
- Monoid
- Groupoid

- $Z$ is a group under ——
- Subtraction
- Division
- Multiplication
- Addition

- $\{3n, n \in z\}$ is an ablian group under ——
- Addition
- Subtraction
- Division
- None of these

- A semi group is always a —–
- Group
- Groupoid
- Monoid
- Addition

- The one-one function is —–
- Straight line
- Circle
- Parabola
- 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