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Previous GATE
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Previous GATE Questions in Discrete Mathematics
36
votes
6
answers
61
GATE CSE 2017 Set 2 | Question: 21
Consider the set $X=\{a, b, c, d, e\}$ under partial ordering $R=\{(a,a), (a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d), (d, e), (e, e) \}$ The Hasse diagram of the partial order $(X, R)$ is shown below. The minimum number of ordered pairs that need to be added to $R$ to make $(X, R)$ a lattice is ______
khushtak
asked
in
Set Theory & Algebra
Feb 14, 2017
by
khushtak
11.8k
views
gatecse-2017-set2
set-theory&algebra
lattice
numerical-answers
normal
39
votes
5
answers
62
GATE CSE 2017 Set 2 | Question: 24
Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____
khushtak
asked
in
Set Theory & Algebra
Feb 14, 2017
by
khushtak
14.3k
views
gatecse-2017-set2
polynomials
numerical-answers
set-theory&algebra
57
votes
10
answers
63
GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
khushtak
asked
in
Mathematical Logic
Feb 14, 2017
by
khushtak
12.1k
views
gatecse-2017-set2
mathematical-logic
propositional-logic
1
vote
1
answer
64
GATE CSE 1988 | Question: 14ii
Consider the following well-formed formula: $\exists x \forall y [ \neg \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$ Show using resolution principle that the well-formed formula, given above, cannot be satisfied for any interpretation.
go_editor
asked
in
Mathematical Logic
Dec 20, 2016
by
go_editor
667
views
gate1988
descriptive
first-order-logic
clausal-form
out-of-gate-syllabus
1
vote
1
answer
65
GATE CSE 1988 | Question: 14i
Consider the following well-formed formula: $\exists x \forall y [ \neg \: \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(x,y)]$ Express the above well-formed formula in clausal form.
go_editor
asked
in
Mathematical Logic
Dec 20, 2016
by
go_editor
653
views
gate1988
descriptive
first-order-logic
clausal-form
out-of-gate-syllabus
7
votes
3
answers
66
GATE CSE 1988 | Question: 13iii
Are the two digraphs shown in the above figure isomorphic? Justify your answer.
go_editor
asked
in
Graph Theory
Dec 20, 2016
by
go_editor
1.2k
views
normal
gate1988
descriptive
graph-theory
graph-isomorphism
out-of-gate-syllabus
25
votes
2
answers
67
GATE CSE 1988 | Question: 13ii
If the set $S$ has a finite number of elements, prove that if $f$ maps $S$ onto $S$, then $f$ is one-to-one.
go_editor
asked
in
Set Theory & Algebra
Dec 20, 2016
by
go_editor
2.6k
views
gate1988
descriptive
set-theory&algebra
functions
1
vote
1
answer
68
GATE CSE 1988 | Question: 13ic
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $f(x)=x^3$, for all $x$ belonging to $G$.
go_editor
asked
in
Set Theory & Algebra
Dec 20, 2016
by
go_editor
547
views
gate1988
normal
descriptive
group-theory
group-homomorphism
out-of-gate-syllabus
1
vote
0
answers
69
GATE CSE 1988 | Question: 13ib
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $\overline{G}=G$
go_editor
asked
in
Graph Theory
Dec 20, 2016
by
go_editor
485
views
gate1988
normal
descriptive
group-theory
group-homomorphism
out-of-gate-syllabus
1
vote
0
answers
70
GATE CSE 1988 | Question: 13ia
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $G$ is the group of non zero real numbers under multiplication.
go_editor
asked
in
Set Theory & Algebra
Dec 20, 2016
by
go_editor
445
views
gate1988
normal
descriptive
group-theory
group-homomorphism
out-of-gate-syllabus
14
votes
2
answers
71
GATE CSE 1988 | Question: 2xviii
Show that if $G$ is a group such that $(a. b)^2 = a^2.b^2$ for all $a, b$ belonging to $G$, then $G$ is an abelian.
go_editor
asked
in
Set Theory & Algebra
Dec 19, 2016
by
go_editor
1.7k
views
gate1988
descriptive
group-theory
15
votes
4
answers
72
GATE CSE 1988 | Question: 2xvi
Write the adjacency matrix representation of the graph given in below figure.
go_editor
asked
in
Graph Theory
Dec 19, 2016
by
go_editor
3.9k
views
gate1988
descriptive
graph-theory
graph-connectivity
13
votes
3
answers
73
GATE CSE 1988 | Question: 2vii
Define the validity of a well-formed formula(wff)?
go_editor
asked
in
Mathematical Logic
Dec 18, 2016
by
go_editor
1.8k
views
gate1988
descriptive
mathematical-logic
propositional-logic
29
votes
4
answers
74
GATE CSE 1989 | Question: 14a
Symbolize the expression "Every mother loves her children" in predicate logic.
makhdoom ghaya
asked
in
Mathematical Logic
Dec 15, 2016
by
makhdoom ghaya
5.8k
views
gate1989
descriptive
first-order-logic
mathematical-logic
25
votes
4
answers
75
GATE CSE 1989 | Question: 13c
Find the number of single valued functions from set $A$ to another set $B,$ given that the cardinalities of the sets $A$ and $B$ are $m$ and $n$ respectively.
makhdoom ghaya
asked
in
Set Theory & Algebra
Dec 15, 2016
by
makhdoom ghaya
2.8k
views
gate1989
descriptive
functions
set-theory&algebra
0
votes
0
answers
76
GATE CSE 1988 | Question: 2iv
Give one property of the field of real numbers which no longer holds when we compute using finite-precision floating point numbers.
go_editor
asked
in
Set Theory & Algebra
Dec 11, 2016
by
go_editor
482
views
gate1988
descriptive
set-theory&algebra
fields
out-of-gate-syllabus
20
votes
6
answers
77
GATE CSE 1988 | Question: 1vii
The complement(s) of the element $'a'$ in the lattice shown in below figure is (are) ____
go_editor
asked
in
Set Theory & Algebra
Dec 10, 2016
by
go_editor
4.6k
views
gate1988
descriptive
lattice
set-theory&algebra
37
votes
5
answers
78
GATE CSE 1989 | Question: 4-i
How many substrings (of all lengths inclusive) can be formed from a character string of length $n$? Assume all characters to be distinct, prove your answer.
makhdoom ghaya
asked
in
Combinatory
Nov 29, 2016
by
makhdoom ghaya
6.9k
views
gate1989
descriptive
combinatory
normal
proof
31
votes
4
answers
79
GATE CSE 1989 | Question: 3-vi
Which of the following graphs is/are planar?
makhdoom ghaya
asked
in
Graph Theory
Nov 27, 2016
by
makhdoom ghaya
7.8k
views
gate1989
normal
graph-theory
graph-planarity
descriptive
18
votes
7
answers
80
GATE CSE 1989 | Question: 3-v
Which of the following well-formed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$
makhdoom ghaya
asked
in
Mathematical Logic
Nov 27, 2016
by
makhdoom ghaya
3.6k
views
gate1989
normal
mathematical-logic
propositional-logic
multiple-selects
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