====== 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