Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Filter
Recent
Hot!
Most votes
Most answers
Most views
Previous GATE
Featured
Previous GATE Questions in Discrete Mathematics
26
votes
8
answers
151
GATE CSE 1996 | Question: 1.1
Let $A$ and $B$ be sets and let $A^c$ and $B^c$ denote the complements of the sets $A$ and $B$. The set $(A-B) \cup (B-A) \cup (A \cap B)$ is equal to $A \cup B$ $A^c \cup B^c$ $A \cap B$ $A^c \cap B^c$
Let $A$ and $B$ be sets and let $A^c$ and $B^c$ denote the complements of the sets $A$ and $B$. The set $(A-B) \cup (B-A) \cup (A \cap B)$ is equal to$A \cup B$$A^c \cup ...
Kathleen
6.0k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
easy
set-theory
+
–
19
votes
3
answers
152
GATE CSE 1995 | Question: 24
Prove that in finite graph, the number of vertices of odd degree is always even.
Prove that in finite graph, the number of vertices of odd degree is always even.
Kathleen
5.7k
views
Kathleen
asked
Oct 8, 2014
Graph Theory
gate1995
graph-theory
degree-of-graph
proof
descriptive
+
–
11
votes
3
answers
153
GATE CSE 1995 | Question: 23
Prove using mathematical induction for $n \geq 5, 2^n > n^2$
Prove using mathematical induction for $n \geq 5, 2^n n^2$
Kathleen
1.5k
views
Kathleen
asked
Oct 8, 2014
Set Theory & Algebra
gate1995
set-theory&algebra
proof
mathematical-induction
descriptive
+
–
27
votes
5
answers
154
GATE CSE 1995 | Question: 21
Let $G_1$ and $G_2$ be subgroups of a group $G$. Show that $G_1 \cap G_2$ is also a subgroup of $G$. Is $G_1 \cup G_2$ always a subgroup of $G$?.
Let $G_1$ and $G_2$ be subgroups of a group $G$.Show that $G_1 \cap G_2$ is also a subgroup of $G$.Is $G_1 \cup G_2$ always a subgroup of $G$?.
Kathleen
6.5k
views
Kathleen
asked
Oct 8, 2014
Set Theory & Algebra
gate1995
set-theory&algebra
group-theory
normal
descriptive
proof
+
–
21
votes
3
answers
155
GATE CSE 1995 | Question: 13
Obtain the principal (canonical) conjunctive normal form of the propositional formula $(p \wedge q) \vee (\neg q \wedge r)$ where $\wedge$ is logical and, $\vee$ is inclusive or and $\neg$ is negation.
Obtain the principal (canonical) conjunctive normal form of the propositional formula $$(p \wedge q) \vee (\neg q \wedge r)$$ where $\wedge$ is logical and, $\vee$ is inc...
Kathleen
4.2k
views
Kathleen
asked
Oct 8, 2014
Mathematical Logic
gate1995
mathematical-logic
propositional-logic
normal
descriptive
+
–
6
votes
2
answers
156
GATE CSE 1995 | Question: 7(A)
Determine the number of divisors of $600.$
Determine the number of divisors of $600.$
Kathleen
1.8k
views
Kathleen
asked
Oct 8, 2014
Set Theory & Algebra
gate1995
set-theory&algebra
number-theory
numerical-answers
+
–
41
votes
4
answers
157
GATE CSE 1995 | Question: 2.19
If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where $\lnot$ is negation, $\lor$ is inclusive OR and $\to$ is implication, is True Multiple Values False Cannot be determined
If the proposition $\lnot p \to q$ is true, then the truth value of the proposition $\lnot p \lor \left ( p \to q \right )$, where $\lnot$ is negation, $\lor$ is inclusiv...
Kathleen
8.5k
views
Kathleen
asked
Oct 8, 2014
Mathematical Logic
gate1995
mathematical-logic
normal
propositional-logic
+
–
27
votes
4
answers
158
GATE CSE 1995 | Question: 2.17
Let $A$ be the set of all non-singular matrices over real number and let $*$ be the matrix multiplication operation. Then $A$ is closed under $*$ but $\langle A, *\rangle$ is not a semigroup. $\langle A, *\rangle$ is a semigroup but not a monoid. $\langle A, * \rangle$ is a monoid but not a group. $\langle A, *\rangle$ is a a group but not an abelian group.
Let $A$ be the set of all non-singular matrices over real number and let $*$ be the matrix multiplication operation. Then$A$ is closed under $*$ but $\langle A, *\rangle$...
Kathleen
9.8k
views
Kathleen
asked
Oct 8, 2014
Set Theory & Algebra
gate1995
set-theory&algebra
group-theory
+
–
33
votes
5
answers
159
GATE CSE 1995 | Question: 1.25
The minimum number of edges in a connected cyclic graph on $n$ vertices is: $n-1$ $n$ $n+1$ None of the above
The minimum number of edges in a connected cyclic graph on $n$ vertices is:$n-1$$n$$n+1$None of the above
Kathleen
21.0k
views
Kathleen
asked
Oct 8, 2014
Graph Theory
gate1995
graph-theory
graph-connectivity
easy
+
–
24
votes
6
answers
160
GATE CSE 1995 | Question: 1.20
The number of elements in the power set $P(S)$ of the set $S=\{\{\emptyset\}, 1, \{2, 3\}\}$ is: $2$ $4$ $8$ None of the above
The number of elements in the power set $P(S)$ of the set $S=\{\{\emptyset\}, 1, \{2, 3\}\}$ is:$2$$4$$8$None of the above
Kathleen
16.2k
views
Kathleen
asked
Oct 8, 2014
Set Theory & Algebra
gate1995
set-theory&algebra
normal
set-theory
+
–
28
votes
6
answers
161
GATE CSE 1995 | Question: 1.19
Let $R$ be a symmetric and transitive relation on a set $A$. Then $R$ is reflexive and hence an equivalence relation $R$ is reflexive and hence a partial order $R$ is reflexive and hence not an equivalence relation None of the above
Let $R$ be a symmetric and transitive relation on a set $A$. Then$R$ is reflexive and hence an equivalence relation$R$ is reflexive and hence a partial order$R$ is reflex...
Kathleen
14.2k
views
Kathleen
asked
Oct 8, 2014
Set Theory & Algebra
gate1995
set-theory&algebra
relations
normal
+
–
3
votes
0
answers
162
GATE CSE 1994 | Question: 16
Every element $a$ of some ring $(R, +, o)$ satisfies the equation $a\;o\;a=a$. Decide whether or not the ring is commutative.
Every element $a$ of some ring $(R, +, o)$ satisfies the equation $a\;o\;a=a$. Decide whether or not the ring is commutative.
Kathleen
539
views
Kathleen
asked
Oct 5, 2014
Set Theory & Algebra
gate1994
set-theory&algebra
ring
normal
out-of-gate-syllabus
descriptive
+
–
18
votes
2
answers
163
GATE CSE 1994 | Question: 15
Use the patterns given to prove that $\sum\limits_{i=0}^{n-1} (2i+1) = n^2$ (You are not permitted to employ induction) Use the result obtained in (A) to prove that $\sum\limits_{i=1}^{n} i = \frac{n(n+1)}{2}$
Use the patterns given to prove that$\sum\limits_{i=0}^{n-1} (2i+1) = n^2$(You are not permitted to employ induction)Use the result obtained in (A) to prove that $\sum\li...
Kathleen
2.0k
views
Kathleen
asked
Oct 5, 2014
Combinatory
gate1994
combinatory
proof
summation
descriptive
+
–
22
votes
3
answers
164
GATE CSE 1994 | Question: 3.13
Let $p$ and $q$ be propositions. Using only the Truth Table, decide whether $p \Longleftrightarrow q$ does not imply $p \to \lnot q$ is True or False.
Let $p$ and $q$ be propositions. Using only the Truth Table, decide whether $p \Longleftrightarrow q$ does not imply $p \to \lnot q$is True or False.
Kathleen
7.2k
views
Kathleen
asked
Oct 5, 2014
Mathematical Logic
gate1994
mathematical-logic
normal
propositional-logic
true-false
+
–
21
votes
5
answers
165
GATE CSE 1994 | Question: 3.9
Every subset of a countable set is countable. State whether the above statement is true or false with reason.
Every subset of a countable set is countable.State whether the above statement is true or false with reason.
Kathleen
3.0k
views
Kathleen
asked
Oct 5, 2014
Set Theory & Algebra
gate1994
set-theory&algebra
normal
set-theory
countable-uncountable-set
true-false
+
–
17
votes
4
answers
166
GATE CSE 1994 | Question: 2.9
The Hasse diagrams of all the lattices with up to four elements are ________ (write all the relevant Hasse diagrams)
The Hasse diagrams of all the lattices with up to four elements are ________ (write all the relevant Hasse diagrams)
Kathleen
4.4k
views
Kathleen
asked
Oct 4, 2014
Set Theory & Algebra
gate1994
set-theory&algebra
lattice
normal
fill-in-the-blanks
+
–
19
votes
3
answers
167
GATE CSE 1994 | Question: 2.5
The number of edges in a regular graph of degree $d$ and $n$ vertices is ____________
The number of edges in a regular graph of degree $d$ and $n$ vertices is ____________
Kathleen
8.0k
views
Kathleen
asked
Oct 4, 2014
Graph Theory
gate1994
graph-theory
easy
graph-connectivity
fill-in-the-blanks
+
–
31
votes
4
answers
168
GATE CSE 1994 | Question: 2.4
The number of subsets $\left\{ 1,2, \dots, n\right\}$ with odd cardinality is ___________
The number of subsets $\left\{ 1,2, \dots, n\right\}$ with odd cardinality is ___________
Kathleen
5.5k
views
Kathleen
asked
Oct 4, 2014
Set Theory & Algebra
gate1994
set-theory&algebra
easy
set-theory
fill-in-the-blanks
+
–
23
votes
3
answers
169
GATE CSE 1994 | Question: 2.3
Amongst the properties $\left\{\text{reflexivity, symmetry, anti-symmetry, transitivity}\right\}$ the relation $R=\{(x, y) \in N^2|x \neq y\}$ satisfies _________
Amongst the properties $\left\{\text{reflexivity, symmetry, anti-symmetry, transitivity}\right\}$ the relation $R=\{(x, y) \in N^2|x \neq y\}$ satisfies _________
Kathleen
5.0k
views
Kathleen
asked
Oct 4, 2014
Set Theory & Algebra
gate1994
set-theory&algebra
normal
relations
fill-in-the-blanks
+
–
39
votes
4
answers
170
GATE CSE 1994 | Question: 2.2
On the set $N$ of non-negative integers, the binary operation ______ is associative and non-commutative.
On the set $N$ of non-negative integers, the binary operation ______ is associative and non-commutative.
Kathleen
5.7k
views
Kathleen
asked
Oct 4, 2014
Set Theory & Algebra
gate1994
set-theory&algebra
normal
group-theory
binary-operation
fill-in-the-blanks
+
–
Page:
« prev
1
...
3
4
5
6
7
8
9
10
11
12
13
...
19
next »
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register