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