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Search results for set-theory&algebra
10
votes
2
answers
21
GATE CSE 2023 | Question: 41
Let $X$ be a set and $2^{X}$ denote the powerset of $X$. Define a binary operation $\Delta$ on $2^{X}$ as follows: \[ A \Delta B=(A-B) \cup(B-A) \text {. } \] Let $H=\left(2^{X}, \Delta\right)$. Which of the following statements about $H$ is/are correct? ... $A \in 2^{X},$ the inverse of $A$ is the complement of $A$. For every $A \in 2^{X},$ the inverse of $A$ is $A$.
Let $X$ be a set and $2^{X}$ denote the powerset of $X$.Define a binary operation $\Delta$ on $2^{X}$ as follows:\[A \Delta B=(A-B) \cup(B-A) \text {. }\]Let $H=\left(2^{...
admin
5.6k
views
admin
asked
Feb 15, 2023
Set Theory & Algebra
gatecse-2023
set-theory&algebra
group-theory
multiple-selects
2-marks
+
–
29
votes
6
answers
22
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
14.4k
views
Kathleen
asked
Oct 8, 2014
Set Theory & Algebra
gate1995
set-theory&algebra
relations
normal
+
–
38
votes
9
answers
23
GATE CSE 2019 | Question: 10
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ ... $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
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 ...
Arjun
17.4k
views
Arjun
asked
Feb 7, 2019
Set Theory & Algebra
gatecse-2019
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
1-mark
+
–
60
votes
9
answers
24
GATE CSE 2005 | Question: 44
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$ $4$ $6$ $16$ $24$
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such th...
gatecse
13.5k
views
gatecse
asked
Sep 21, 2014
Combinatory
gatecse-2005
set-theory&algebra
normal
pigeonhole-principle
+
–
39
votes
5
answers
25
GATE CSE 2000 | Question: 2.5
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true? $R$ is not an equivalence relation $R$ is an equivalence relation having $1$ equivalence class $R$ is an equivalence relation having $2$ equivalence classes $R$ is an equivalence relation having $3$ equivalence classes
A relation $R$ is defined on the set of integers as $xRy$ iff $(x + y)$ is even. Which of the following statements is true?$R$ is not an equivalence relation$R$ is an equ...
Kathleen
14.1k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2000
set-theory&algebra
relations
normal
+
–
40
votes
5
answers
26
GATE CSE 1996 | Question: 2.2
Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement) $A$ is reflexive and transitive $R$ is symmetric and not transitive $R$ is an equivalence relation $R$ is not reflexive and not symmetric
Let $R$ be a non-empty relation on a collection of sets defined by $_{A}R_ B$ if and only if $A \cap B = \phi$. Then, (pick the true statement)$A$ is reflexive and transi...
Kathleen
14.0k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
relations
normal
+
–
41
votes
3
answers
27
GATE CSE 2007 | Question: 26
Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on $S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overline{cd}\},$ ... $π_i \prec π_j$ if and only if $π_i$ refines $π_j$. The poset diagram for $(S',\prec)$ is:
Consider the set $S =\{ a , b , c , d\}.$ Consider the following $4$ partitions $π_1,π_2,π_3,π_4$ on$S : π_1 =\{\overline{abcd}\},\quad π_2 =\{\overline{ab}, \overl...
Kathleen
13.5k
views
Kathleen
asked
Sep 21, 2014
Set Theory & Algebra
gatecse-2007
set-theory&algebra
normal
partial-order
descriptive
+
–
36
votes
6
answers
28
GATE CSE 2005 | Question: 7
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be: $O(n)$ $O(n \log n)$ $O \left( n^{\frac{3}{2}} \right)$ $O\left(n^3\right)$
The time complexity of computing the transitive closure of a binary relation on a set of $n$ elements is known to be:$O(n)$$O(n \log n)$$O \left( n^{\frac{3}{2}} \right)...
Kathleen
24.7k
views
Kathleen
asked
Sep 22, 2014
Set Theory & Algebra
gatecse-2005
set-theory&algebra
normal
relations
+
–
77
votes
9
answers
29
GATE CSE 2006 | Question: 25
Let $S = \{1, 2, 3,\ldots, m\}, m >3.$ Let $X_1,\ldots,X_n$ be subsets of $S$ each of size $3.$ Define a function $f$ from $S$ to the set of natural numbers as, $f(i)$ is the number of sets $X_j$ that contain the element $i.$ That is $f(i)=\left | \left\{j \mid i\in X_j \right\} \right|$ then $ \sum_{i=1}^{m} f(i)$ is: $3m$ $3n$ $2m+1$ $2n+1$
Let $S = \{1, 2, 3,\ldots, m\}, m >3.$ Let $X_1,\ldots,X_n$ be subsets of $S$ each of size $3.$ Define a function $f$ from $S$ to the set of natural numbers as, $f(i)$ is...
Rucha Shelke
11.1k
views
Rucha Shelke
asked
Sep 18, 2014
Set Theory & Algebra
gatecse-2006
set-theory&algebra
normal
functions
+
–
42
votes
8
answers
30
GATE CSE 2004 | Question: 73
The inclusion of which of the following sets into $S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3, 4, 5\right\} \right\} $ is necessary and sufficient to make $S$ a complete lattice under the partial order defined by ... $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$
The inclusion of which of the following sets into$S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3,...
Kathleen
12.9k
views
Kathleen
asked
Sep 18, 2014
Set Theory & Algebra
gatecse-2004
set-theory&algebra
partial-order
normal
+
–
60
votes
6
answers
31
GATE CSE 2014 Set 1 | Question: 50
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is _______.
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is...
go_editor
12.5k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set1
set-theory&algebra
functions
combinatory
numerical-answers
+
–
58
votes
6
answers
32
GATE CSE 2003 | Question: 31
Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S \(\to\) {True, False} be a predicate defined on S. Suppose that P(a) = True, P(b) = False and P(x) \(\implies\) P(y) for all $x, y \in S$ satisfying $x \leq y$ ... for all x \(\in\) S such that b ≤ x and x ≠ c P(x) = False for all x \(\in\) S such that a ≤ x and b ≤ x
Let $(S, \leq)$ be a partial order with two minimal elements a and b, and a maximum element c. Let P: S \(\to\) {True, False} be a predicate defined on S. Suppose that P(...
Kathleen
11.8k
views
Kathleen
asked
Sep 16, 2014
Set Theory & Algebra
gatecse-2003
set-theory&algebra
partial-order
normal
propositional-logic
+
–
22
votes
5
answers
33
GATE CSE 1996 | Question: 1.2
Let $X = \{2, 3, 6, 12, 24\}$, Let $\leq$ be the partial order defined by $X \leq Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X, \leq)$ is $3$ $4$ $9$ None of the above
Let $X = \{2, 3, 6, 12, 24\}$, Let $\leq$ be the partial order defined by $X \leq Y$ if $x$ divides $y$. Number of edges in the Hasse diagram of $(X, \leq)$ is$3$$4$$9$No...
Kathleen
13.4k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
partial-order
normal
+
–
45
votes
10
answers
34
GATE IT 2005 | Question: 33
Let $A$ be a set with $n$ elements. Let $C$ be a collection of distinct subsets of $A$ such that for any two subsets $S_1$ and $S_2$ in $C$, either $S_1 \subset S_2$ or $S_2\subset S_1$. What is the maximum cardinality of $C?$ $n$ $n+1$ $2^{n-1} + 1$ $n!$
Let $A$ be a set with $n$ elements. Let $C$ be a collection of distinct subsets of $A$ such that for any two subsets $S_1$ and $S_2$ in $C$, either $S_1 \subset S_2$ or $...
Ishrat Jahan
11.9k
views
Ishrat Jahan
asked
Nov 3, 2014
Set Theory & Algebra
gateit-2005
set-theory&algebra
normal
set-theory
+
–
43
votes
9
answers
35
GATE CSE 1996 | Question: 2.1
Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, x-y)$. The inverse function of $f$ is given by $f^{-1} (x,y) = \left( \frac {1}{x+y}, \frac{1}{x-y}\right)$ ... $f^{-1}(x,y)=\left [ 2\left(x-y\right),2\left(x+y\right) \right ]$
Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, x-y)$. The inverse function of $f$ is ...
Kathleen
9.8k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
functions
normal
+
–
49
votes
5
answers
36
GATE CSE 2001 | Question: 2.3
Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images. $S_1: f(E \cup F) = f(E) \cup f(F)$ $S_2: f(E \cap F)=f(E) \cap f(F)$ Which of the following is true about S1 and S2? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct
Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images.$S_1: f(E \cup F) = f(E) \cup f(F)$$S_2: f(E \cap F...
Kathleen
11.2k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2001
set-theory&algebra
functions
normal
+
–
29
votes
6
answers
37
GATE CSE 2002 | Question: 2.17
The binary relation $S= \phi \text{(empty set)}$ on a set $A = \left \{ 1,2,3 \right \}$ is Neither reflexive nor symmetric Symmetric and reflexive Transitive and reflexive Transitive and symmetric
The binary relation $S= \phi \text{(empty set)}$ on a set $A = \left \{ 1,2,3 \right \}$ is Neither reflexive nor symmetricSymmetric and reflexiveTransitive and reflexive...
Kathleen
12.9k
views
Kathleen
asked
Sep 15, 2014
Set Theory & Algebra
gatecse-2002
set-theory&algebra
normal
relations
+
–
32
votes
7
answers
38
GATE IT 2007 | Question: 23
A partial order $P$ is defined on the set of natural numbers as follows. Here $\frac{x}{y}$ denotes integer division. $(0, 0) \in P.$ $(a, b) \in P$ if and only if $(a \% 10) \leq (b \% 10$) and $(\frac{a}{10},\frac{b}{10})\in P.$ ... $P$? (i) and (iii) (ii) and (iv) (i) and (iv) (iii) and (iv)
A partial order $P$ is defined on the set of natural numbers as follows. Here $\frac{x}{y}$ denotes integer division.$(0, 0) \in P.$$(a, b) \in P$ if and only if $(a \% 1...
Ishrat Jahan
11.4k
views
Ishrat Jahan
asked
Oct 29, 2014
Set Theory & Algebra
gateit-2007
set-theory&algebra
partial-order
normal
+
–
42
votes
3
answers
39
GATE CSE 1994 | Question: 1.10
Some group $(G, o)$ is known to be abelian. Then, which one of the following is true for $G$? $g=g^{-1} \text{ for every } g \in G$ $g=g^2 \text{ for every }g \in G$ $(goh)^2 = g^2oh^2 \text{ for every } g, h \in G$ $G$ is of finite order
Some group $(G, o)$ is known to be abelian. Then, which one of the following is true for $G$?$g=g^{-1} \text{ for every } g \in G$$g=g^2 \text{ for every }g \in G$$(goh)...
Kathleen
10.7k
views
Kathleen
asked
Oct 4, 2014
Set Theory & Algebra
gate1994
set-theory&algebra
group-theory
normal
+
–
3
votes
2
answers
40
GATE CSE 2024 | Set 1 | Question: 42
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE? Operator $\diamond$ ... $\square$ obeys the distributive law Operator $\square$ over the operator $\diamond$ obeys the distributive law
Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE?Ope...
Arjun
1.8k
views
Arjun
asked
Feb 16
Set Theory & Algebra
gatecse2024-set1
multiple-selects
set-theory&algebra
+
–
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