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Previous GATE Questions in Set Theory & Algebra
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Previous GATE
Recent
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Previous GATE
+5
votes
2
answers
1
GATE199525b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
asked
Jun 6, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

410
views
gate1995
settheory&algebra
numericalanswers
sets
+11
votes
3
answers
2
GATE201910
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{1}bg$ $R_2: \forall a , b \in G, \: a R_2 b \text{ if and only if } a= b^{1}$ Which of the above is/are equivalence relation/relations? $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
asked
Feb 7, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

3.5k
views
gate2019
engineeringmathematics
discretemathematics
settheory&algebra
grouptheory
+3
votes
2
answers
3
GATE199810b
Let $R$ be a binary relation on $A = \{a, b, c, d, e, f, g, h\}$ represented by the following two component digraph. Find the smallest integers $m$ and $n$ such that $m < n$ and $R^m = R^n$.
asked
Aug 12, 2018
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

398
views
gate1998
descriptive
settheory&algebra
relations
+27
votes
5
answers
4
GATE201827
Let $N$ be the set of natural numbers. Consider the following sets, $P:$ Set of Rational numbers (positive and negative) $Q:$ Set of functions from $\{0,1\}$ to $N$ $R:$ Set of functions from $N$ to $\{0, 1\}$ $S:$ Set of finite subsets of $N$ Which of the above sets are countable? $Q$ and $S$ only $P$ and $S$ only $P$ and $R$ only $P, Q$ and $S$ only
asked
Feb 14, 2018
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

5.6k
views
gate2018
settheory&algebra
countableuncountableset
normal
+12
votes
4
answers
5
GATE201819
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
asked
Feb 14, 2018
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

3.9k
views
gate2018
grouptheory
numericalanswers
settheory&algebra
+16
votes
8
answers
6
GATE2017147
The number of integers between $1$ and $500$ (both inclusive) that are divisible by $3$ or $5$ or $7$ is ____________ .
asked
Feb 14, 2017
in
Set Theory & Algebra
by
Arjun
Veteran
(
431k
points)

3.8k
views
gate20171
settheory&algebra
normal
numericalanswers
sets
+25
votes
4
answers
7
GATE2017221
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 ______
asked
Feb 14, 2017
in
Set Theory & Algebra
by
khushtak
Loyal
(
7.1k
points)

4.1k
views
gate20172
settheory&algebra
lattice
numericalanswers
normal
+24
votes
5
answers
8
GATE2017224
Consider the quadratic equation $x^213x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b=$ _____
asked
Feb 14, 2017
in
Set Theory & Algebra
by
khushtak
Loyal
(
7.1k
points)

4.5k
views
gate20172
polynomials
numericalanswers
settheory&algebra
+13
votes
1
answer
9
GATE198813ii
If the set $S$ has a finite number of elements, prove that if $f$ maps $S$ onto $S$, then $f$ is onetoone.
asked
Dec 20, 2016
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

614
views
gate1988
descriptive
settheory&algebra
functions
0
votes
0
answers
10
GATE198813ic
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $f(x)=x^3$, for all $x$ belonging to $G$.
asked
Dec 20, 2016
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

145
views
gate1988
normal
descriptive
grouptheory
grouphomomorphism
nongate
0
votes
0
answers
11
GATE198813ia
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $G$ is the group of non zero real numbers under multiplication.
asked
Dec 20, 2016
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

124
views
gate1988
normal
descriptive
grouptheory
grouphomomorphism
nongate
+2
votes
1
answer
12
GATE19882xviii
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.
asked
Dec 19, 2016
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

266
views
gate1988
descriptive
grouptheory
+17
votes
3
answers
13
GATE198913c
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.
asked
Dec 16, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

630
views
gate1989
descriptive
functions
0
votes
0
answers
14
GATE19882iv
Give one property of the field of real numbers which no longer holds when we compute using finiteprecision floating point numbers.
asked
Dec 11, 2016
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

117
views
gate1988
descriptive
settheory&algebra
fields
nongate
+11
votes
2
answers
15
GATE19881vii
The complement(s) of the element 'a' in the lattice shown in below figure is (are) ____
asked
Dec 10, 2016
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

1k
views
gate1988
descriptive
lattice
settheory&algebra
+28
votes
1
answer
16
GATE19891v
The number of possible commutative binary operations that can be defined on a set of $n$ elements (for a given n) is ___________.
asked
Nov 27, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

1.9k
views
gate1989
descriptive
settheory&algebra
binaryoperation
+14
votes
4
answers
17
GATE19891iv
The transitive closure of the relation $\left\{(1, 2), (2, 3), (3, 4), (5, 4)\right\}$ on the set $\left\{1, 2, 3, 4, 5\right\}$ is ___________.
asked
Nov 27, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

933
views
gate1989
settheory&algebra
relations
descriptive
+1
vote
2
answers
18
GATE199017c
Show that the elements of the lattice $(N, \leq)$, where $N$ is the set of positive intergers and $a \leq b$ if and only if $a$ divides $b$, satisfy the distributive property.
asked
Nov 27, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

307
views
gate1990
descriptive
settheory&algebra
lattice
+11
votes
2
answers
19
GATE19902x
Match the pairs in the following questions:$\begin{array}{llll}\hline (a) & \text{Groups} & (p) & \text{Associativity} \\\hline (b) & \text{Semigroups} & (q) & \text{Identity} \\\hline (c) & \text{Monoids} & (r) & \text{Commutativity} \\\hline (d) & \text{Abelian groups} & (s) & \text{Left inverse} \\\hline \end{array}$
asked
Nov 19, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

798
views
gate1990
matchthefollowing
settheory&algebra
grouptheory
+2
votes
1
answer
20
GATE19879f
Give the composition tables (Cayley Tables) of the two non isomorphic groups of order 4 with elements $e, a, b, c$ where $c$ is the identity element. Use the order $e, a, b, c$ for the rows and columns.
asked
Nov 15, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

216
views
gate1987
groupisomorphism
settheory&algebra
nongate
+7
votes
1
answer
21
GATE19879e
How many true inclusion relations are there of the from $A \subseteq B$, where $A$ and $B$ are subsets of a set $S$ with $n$ elements?
asked
Nov 15, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

573
views
gate1987
settheory&algebra
relations
+16
votes
2
answers
22
GATE19879b
How many onetoone functions are there from a set $A$ with $n$ elements onto itself?
asked
Nov 15, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

901
views
gate1987
settheory&algebra
functions
descriptive
+11
votes
2
answers
23
GATE19879a
How many binary relations are there on a set $A$ with $n$ elements?
asked
Nov 15, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

1k
views
gate1987
settheory&algebra
relations
descriptive
+10
votes
3
answers
24
GATE19872d
State whether the following statements are TRUE or FALSE: The union of two equivalence relations is also an equivalence relation.
asked
Nov 9, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

1.2k
views
gate1987
discretemathematics
relations
descriptive
+10
votes
4
answers
25
GATE19871xxii
The equation $7x^{7}+14x^{6}+12x^{5}+3x^{4}+12x^{3}+10x^{2}+5x+7=0$ has All complex roots At least one real root Four pairs of imaginary roots None of the above
asked
Nov 9, 2016
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
30.8k
points)

521
views
gate1987
polynomials
+15
votes
2
answers
26
GATE199214b
Consider the set of integers $\{1,2,3,4,6,8,12,24\}$ together with the two binary operations LCM (lowest common multiple) and GCD (greatest common divisor). Which of the following algebraic structures does this represent? group ring field lattice
asked
Apr 24, 2016
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

1.2k
views
gate1992
settheory&algebra
grouptheory
normal
0
votes
1
answer
27
GATE199215.b
Let $S$ be the set of all integers and let $n > 1$ be a fixed integer. Define for $a,b \in S, a R b$ iff $ab$ is a multiple of $n$. Show that $R$ is an equivalence relation and find its equivalence classes for $n = 5$.
asked
Apr 24, 2016
in
Set Theory & Algebra
by
jothee
Veteran
(
105k
points)

444
views
gate1992
settheory&algebra
normal
relations
+58
votes
6
answers
28
GATE2016128
A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$,satisfies the following properties: $f(n)=f(n/2)$ if $n$ is even $f(n)=f(n+5)$ if $n$ is odd Let $R=\{ i \mid \exists{j} : f(j)=i \}$ be the set of distinct values that $f$ takes. The maximum possible size of $R$ is ___________.
asked
Feb 12, 2016
in
Set Theory & Algebra
by
Sandeep Singh
Loyal
(
7.2k
points)

6.7k
views
gate20161
settheory&algebra
functions
normal
numericalanswers
+33
votes
6
answers
29
GATE2016226
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? Both $P$ and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
asked
Feb 12, 2016
in
Set Theory & Algebra
by
Akash Kanase
Boss
(
41.9k
points)

4.8k
views
gate20162
settheory&algebra
relations
normal
+55
votes
7
answers
30
GATE2016228
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts with an odd number ... in U \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.
asked
Feb 12, 2016
in
Set Theory & Algebra
by
Akash Kanase
Boss
(
41.9k
points)

5.5k
views
gate20162
settheory&algebra
difficult
sets
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