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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 $A \cup B$ $A^c \cup B^c$ $A \cap B$ $A^c \cap B^c$
Kathleen
asked
in
Set Theory & Algebra
Oct 9, 2014
by
Kathleen
6.0k
views
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.
Kathleen
asked
in
Graph Theory
Oct 8, 2014
by
Kathleen
5.7k
views
gate1995
graph-theory
degree-of-graph
proof
descriptive
11
votes
3
answers
153
GATE CSE 1995 | Question: 23
Prove using mathematical induction for $n \geq 5, 2^n > n^2$
Kathleen
asked
in
Set Theory & Algebra
Oct 8, 2014
by
Kathleen
1.5k
views
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 $G$?.
Kathleen
asked
in
Set Theory & Algebra
Oct 8, 2014
by
Kathleen
6.5k
views
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.
Kathleen
asked
in
Mathematical Logic
Oct 8, 2014
by
Kathleen
4.2k
views
gate1995
mathematical-logic
propositional-logic
normal
descriptive
6
votes
2
answers
156
GATE CSE 1995 | Question: 7(A)
Determine the number of divisors of $600.$
Kathleen
asked
in
Set Theory & Algebra
Oct 8, 2014
by
Kathleen
1.8k
views
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
Kathleen
asked
in
Mathematical Logic
Oct 8, 2014
by
Kathleen
8.5k
views
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.
Kathleen
asked
in
Set Theory & Algebra
Oct 8, 2014
by
Kathleen
9.9k
views
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
Kathleen
asked
in
Graph Theory
Oct 8, 2014
by
Kathleen
21.0k
views
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
Kathleen
asked
in
Set Theory & Algebra
Oct 8, 2014
by
Kathleen
16.2k
views
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
Kathleen
asked
in
Set Theory & Algebra
Oct 8, 2014
by
Kathleen
14.3k
views
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.
Kathleen
asked
in
Set Theory & Algebra
Oct 5, 2014
by
Kathleen
542
views
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 $\sum\limits_{i=1}^{n} i = \frac{n(n+1)}{2}$
Kathleen
asked
in
Combinatory
Oct 5, 2014
by
Kathleen
2.0k
views
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.
Kathleen
asked
in
Mathematical Logic
Oct 5, 2014
by
Kathleen
7.3k
views
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.
Kathleen
asked
in
Set Theory & Algebra
Oct 5, 2014
by
Kathleen
3.0k
views
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)
Kathleen
asked
in
Set Theory & Algebra
Oct 4, 2014
by
Kathleen
4.4k
views
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 ____________
Kathleen
asked
in
Graph Theory
Oct 4, 2014
by
Kathleen
8.0k
views
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 ___________
Kathleen
asked
in
Set Theory & Algebra
Oct 4, 2014
by
Kathleen
5.5k
views
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 _________
Kathleen
asked
in
Set Theory & Algebra
Oct 4, 2014
by
Kathleen
5.1k
views
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.
Kathleen
asked
in
Set Theory & Algebra
Oct 4, 2014
by
Kathleen
5.8k
views
gate1994
set-theory&algebra
normal
group-theory
binary-operation
fill-in-the-blanks
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