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Previous GATE
Featured
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 ______
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...
khushtak
12.0k
views
khushtak
asked
Feb 14, 2017
Set Theory & Algebra
gatecse-2017-set2
set-theory&algebra
lattice
numerical-answers
normal
+
–
40
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 $b=$ _____
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
14.5k
views
khushtak
asked
Feb 14, 2017
Set Theory & Algebra
gatecse-2017-set2
polynomials
numerical-answers
set-theory&algebra
+
–
57
votes
10
answers
63
GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
Let $p, q, r$ denote the statements ”It is raining”, “It is cold”, and “It is pleasant”, respectively. Then the statement “It is not raining and it is pleas...
khushtak
12.3k
views
khushtak
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set2
mathematical-logic
propositional-logic
+
–
1
votes
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.
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...
go_editor
702
views
go_editor
asked
Dec 20, 2016
Mathematical Logic
gate1988
descriptive
first-order-logic
clausal-form
out-of-gate-syllabus
+
–
1
votes
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.
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 c...
go_editor
681
views
go_editor
asked
Dec 20, 2016
Mathematical Logic
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.
Are the two digraphs shown in the above figure isomorphic? Justify your answer.
go_editor
1.3k
views
go_editor
asked
Dec 20, 2016
Graph Theory
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.
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
2.6k
views
go_editor
asked
Dec 20, 2016
Set Theory & Algebra
gate1988
descriptive
set-theory&algebra
functions
+
–
1
votes
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 $G$.
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
566
views
go_editor
asked
Dec 20, 2016
Set Theory & Algebra
gate1988
normal
descriptive
group-theory
group-homomorphism
out-of-gate-syllabus
+
–
2
votes
0
answers
69
GATE CSE 1988 | Question: 13ib
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $\overline{G}=G$
Verify whether the following mapping is a homomorphism. If so, determine its kernel.$\overline{G}=G$
go_editor
486
views
go_editor
asked
Dec 20, 2016
Graph Theory
gate1988
normal
descriptive
group-theory
group-homomorphism
out-of-gate-syllabus
+
–
1
votes
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.
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
454
views
go_editor
asked
Dec 20, 2016
Set Theory & Algebra
gate1988
normal
descriptive
group-theory
group-homomorphism
out-of-gate-syllabus
+
–
15
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.
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
1.8k
views
go_editor
asked
Dec 19, 2016
Set Theory & Algebra
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.
Write the adjacency matrix representation of the graph given in below figure.
go_editor
4.0k
views
go_editor
asked
Dec 19, 2016
Graph Theory
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)?
Define the validity of a well-formed formula(wff)?
go_editor
1.9k
views
go_editor
asked
Dec 18, 2016
Mathematical Logic
gate1988
descriptive
mathematical-logic
propositional-logic
+
–
31
votes
5
answers
74
GATE CSE 1989 | Question: 14a
Symbolize the expression "Every mother loves her children" in predicate logic.
Symbolize the expression "Every mother loves her children" in predicate logic.
makhdoom ghaya
6.0k
views
makhdoom ghaya
asked
Dec 15, 2016
Mathematical Logic
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.
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
2.9k
views
makhdoom ghaya
asked
Dec 15, 2016
Set Theory & Algebra
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.
Give one property of the field of real numbers which no longer holds when we compute using finite-precision floating point numbers.
go_editor
496
views
go_editor
asked
Dec 11, 2016
Set Theory & Algebra
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) ____
The complement(s) of the element $'a'$ in the lattice shown in below figure is (are) ____
go_editor
4.6k
views
go_editor
asked
Dec 10, 2016
Set Theory & Algebra
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.
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
7.0k
views
makhdoom ghaya
asked
Nov 29, 2016
Combinatory
gate1989
descriptive
combinatory
normal
proof
+
–
31
votes
4
answers
79
GATE CSE 1989 | Question: 3-vi
Which of the following graphs is/are planar?
Which of the following graphs is/are planar?
makhdoom ghaya
7.9k
views
makhdoom ghaya
asked
Nov 27, 2016
Graph Theory
gate1989
normal
graph-theory
graph-planarity
descriptive
+
–
19
votes
7
answers
80
GATE CSE 1989 | Question: 3-v
Which of the following well-formed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$
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
3.7k
views
makhdoom ghaya
asked
Nov 27, 2016
Mathematical Logic
gate1989
normal
mathematical-logic
propositional-logic
multiple-selects
+
–
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