Recent questions tagged relations

1 votes

1 answer

61

DBMS relational algebra
Information about a collection of students is given by the relation studinfo (studid, name, sex). The relation enroll (studld, Courseld) gives which student has enrolled for (or taken) what course(s). Assume that every course is taken by at least one ... a proper subset of female students are enrolled (c) Courses in which only male students are enrolled (d) None of the above

Information about a collection of students is given by the relation studinfo (studid, name, sex). The relation enroll (studld, Courseld) gives which student has enrolled ...

737 views

rohitkaushal1 asked Sep 25, 2022

0 votes

0 answers

62

Database: Minimum number of tuples
Consider a relation schema r(A, B, C). Number of elements in domain of attributes A, B and C are 4, 10 and 17 respectively. “ Minimum ” number of tuples possible in an instance of relation r is ________.

Consider a relation schema r(A, B, C). Number of elements in domain of attributes A, B and C are 4, 10 and 17 respectively. “ Minimum ” number of tuples possible in a...

719 views

Shreya2002 asked Aug 9, 2022

4 votes

1 answer

63

GO Classes Scholarship 2023 | Test | Question: 1
A relation $\text{R}$ on a set $\text{A}$ is said to be Total Relation iff $a\text{R}b$ Or $b\text{R}a$ Or both, for all $a,b \in \mathrm{A}$. Which of the following options is/are false? Every Total relation is ... total and transitive, then $\mathrm{S}$ is an equivalence relation. The number of total relations on a set of $5$ elements is $1024.$

A relation $\text{R}$ on a set $\text{A}$ is said to be Total Relation iff $a\text{R}b$ Or $b\text{R}a$ Or both, for all $a,b \in \mathrm{A}$.Which of the following optio...

964 views

GO Classes asked Aug 6, 2022

2 votes

3 answers

64

GO Classes Scholarship 2023 | Test | Question: 2
Let $\text{S}$ be the set of all bit-strings of length $7 .$ We define a relation $\mathrm{R}$ on the set $\mathrm{S}$ by the rule that $x\mathrm{R}y$ iff $x$ and $y$ ... such that $\forall j \neq i, x_{j}=y_{j}$ and $x_{i} \neq y_{i}$. What is the cardinality of relation $\mathrm{R}$?

Let $\text{S}$ be the set of all bit-strings of length $7 .$ We define a relation $\mathrm{R}$ on the set $\mathrm{S}$ by the rule that $x\mathrm{R}y$ iff $x$ and $y$ dif...

949 views

GO Classes asked Aug 6, 2022

3 votes

1 answer

65

GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 12

Let $R$ be a relation from a set $A$ to a set $B.$ The inverse relation from $B$ to $A,$ denoted by $R^{-1}$ , is the set of ordered pairs $\{(b,a) \mid (a,b) \in R\}$ .$...

425 views

GO Classes asked May 12, 2022

4 votes

2 answers

66

GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 14

Consider the following sentences :$[R, | ]$ is poset. Where $R$ is the set of all real numbers and $|$ is the divisibility relation i.e. for any $a,b$ in $R, a|b$ iff the...

677 views

GO Classes asked May 12, 2022

3 votes

1 answer

67

GO Classes Weekly Quiz 10 | Discrete Mathematics | Set Theory, Mathematical Logic, Lattice | Question: 15

Suppose $A$ is a finite set of five elements. Then the cardinality of the largest partial order relation possible on $A$ is _______

376 views

GO Classes asked May 12, 2022

3 votes

1 answer

68

GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 1
Consider a Set $\text{X} = \{a, b, c, d, e\}$ and a relation $\text{R}$ defined on $\text{X}:$ $\text{R} = \{(a, a), (a, b), (a, e), (b, b), (b, e), (c, c), (c, d), (d, d), (e, e)\}.$ Which of the following properties is Not true for $\text{R}?$ reflexive symmetric anti-symmetric transitive

Consider a Set $\text{X} = \{a, b, c, d, e\}$ and a relation $\text{R}$ defined on $\text{X}:$$\text{R} = \{(a, a), (a, b), (a, e), (b, b), (b, e), (c, c), (c, d), (d, d)...

271 views

GO Classes asked Apr 21, 2022

5 votes

1 answer

69

GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 5
Let $\text{N}$ be the set of positive integers. Consider the relation $\text{R}$ on $\text{N}$ defined by $x\text{R}y$ if and only if $\gcd(x,y)>1.$ The relation $\text{R}$ on $\text{N}$ is ________ Reflexive Symmetric Transitive Equivalence relation

Let $\text{N}$ be the set of positive integers. Consider the relation $\text{R}$ on $\text{N}$ defined by $x\text{R}y$ if and only if $\gcd(x,y)>1.$The relation $\text{R}...

418 views

GO Classes asked Apr 21, 2022

4 votes

1 answer

70

GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 7
A relation $\text{R}$ on a set $\text{A}$ is said to be triangular iff $a\text{R}b$ and $c\text{R}b$ together imply $a\text{R}c,$ For all $a,b,c \in \text{A} \,\,\,and \,\,\, a \neq c.$ ... $\text{S}$ is a transitive relation. If a relation $\text{S}$ is transitive and triangular, then $\text{S}$ is a symmetric relation.

A relation $\text{R}$ on a set $\text{A}$ is said to be triangular iff $a\text{R}b$ and $c\text{R}b$ together imply $a\text{R}c,$ For all $a,b,c \in \text{A} \,\,\,and \,...

715 views

GO Classes asked Apr 21, 2022

3 votes

1 answer

71

GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 9
We define a relation $\text{S}$ on a non-empty Set $\text{A}.$ The definition of relation $\text{S}$ ... $\text{A}$ on which such relation $\text{S}$ can be defined.

We define a relation $\text{S}$ on a non-empty Set $\text{A}.$ The definition of relation $\text{S}$ is given in form of a first order logic formula below :$$\forall x \f...

572 views

GO Classes asked Apr 21, 2022

7 votes

1 answer

72

GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 16
Let $\text{Z}$ be the set of all integers. Define a relation $\text{S}$ on $\text{Z} \times \text{Z}$ by $(w,x)\text{S}(y,z)$ if and only if $w-x = y-z.$ We know that $\text{S}$ is an equivalence relation. Which of the ... class of $(a,b)$ is disjoint from the equivalence class of $(a-2,b+2),$ for all $a,b,c,d \in \text{Z}.$

Let $\text{Z}$ be the set of all integers. Define a relation $\text{S}$ on $\text{Z} \times \text{Z}$ by $(w,x)\text{S}(y,z)$ if and only if $w-x = y-z.$ We know that $\t...

445 views

GO Classes asked Apr 21, 2022

4 votes

1 answer

73

GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 18
Let $\text{R}$ and $\text{S}$ be binary relations on a set $\text{A}.$ Suppose that $\text{R}$ is reflexive, symmetric, and transitive and that $\text{S}$ is symmetric, and transitive but is not reflexive ... and symmetric but not reflexive $\text{R} \cup \text{S}$ is reflexive and symmetric but may not be transitive.

Let $\text{R}$ and $\text{S}$ be binary relations on a set $\text{A}.$ Suppose that $\text{R}$ is reflexive, symmetric, and transitive and that $\text{S}$ is symmetric, a...

262 views

GO Classes asked Apr 21, 2022

4 votes

3 answers

74

GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 21
Let $\text{A}$ be any set. The following are the definitions of Irreflexive and Asymmetric Relations : A binary relation $\text{R}$ on a set $\text{A}$ ... total order relation. Every strict order is antisymmetric. Every relation which is both Irreflexive and Asymmetric is in strict order.

Let $\text{A}$ be any set.The following are the definitions of Irreflexive and Asymmetric Relations :A binary relation $\text{R}$ on a set $\text{A}$ is irreflexive iff $...

519 views

GO Classes asked Apr 21, 2022

4 votes

2 answers

75

GO Classes 2023 | Weekly Quiz 7 | Question: 5
We defined a new class of relations GO on a Set. A relation $\text{R}$ on a set $\text{A}$ is said to be GO iff $\forall a,b [ (a\text{R}b \wedge b\text{R}a) \leftrightarrow (a=b) ],$ ... correct about relation GO? Every GO relation is reflexive. Every GO relation is symmetric. Every GO relation is anti-symmetric. Every GO relation is transitive.

We defined a new class of relations “GO” on a Set.A relation $\text{R}$ on a set $\text{A}$ is said to be GO iff $\forall a,b [ (a\text{R}b \wedge b\text{R}a) \leftri...

439 views

GO Classes asked Apr 14, 2022

3 votes

1 answer

76

GO Classes 2023 | Weekly Quiz 7 | Question: 9
Let $\text{S}$ be a non-empty set. $\text{P(s)}$ is the power set of $\text{S}.$ Let $\text{A}$ be a non-empty subset of $\text{P(s)}.$ We define is subset of relation $\text{R}$ on $\text{A}.$ So, $x\text{R}y$ iff ... be symmetric, for some choice of $\text{A}.$ It is possible for $\text{R}$ to be Not anti-symmetric, for some choice of $\text{A}.$

Let $\text{S}$ be a non-empty set. $\text{P(s)}$ is the power set of $\text{S}.$Let $\text{A}$ be a non-empty subset of $\text{P(s)}.$We define “is subset of” relatio...

351 views

GO Classes asked Apr 14, 2022

3 votes

1 answer

77

GO Classes 2023 | Weekly Quiz 7 | Question: 10
Consider a set $\text{A} = \{ a,b,c,d,e,f,g \}.$ Consider the following partition $\text{P}$ of set $\text{A}:$ $\text{P} : \{ \{a,b\} , \{c\}, \{d\}, \{e,f,g\} \}$ ... that the set of equivalence classes of $\text{R}$ is exactly the same as partition $\text{P}.$ What is the cardinality of relation $\text{R}?$

Consider a set $\text{A} = \{ a,b,c,d,e,f,g \}.$Consider the following partition $\text{P}$ of set $\text{A}:$$\text{P} : \{ \{a,b\} , \{c\}, \{d\}, \{e,f,g\} \}$We defin...

357 views

GO Classes asked Apr 14, 2022

3 votes

1 answer

78

GO Classes 2023 | Weekly Quiz 7 | Question: 12
Let $\text{A, B}$ be two non-empty sets, with cardinality $3,4$ respectively. Let $\text{R}$ be a relation defined on the power set of $\text{A} \times \text{B}.$ Relation $\text{R}$ is reflexive, symmetric, transitive and antisymmetric. How many equivalence classes does relation $\text{R}$ have?

Let $\text{A, B}$ be two non-empty sets, with cardinality $3,4$ respectively. Let $\text{R}$ be a relation defined on the power set of $\text{A} \times \text{B}.$ Relatio...

703 views

GO Classes asked Apr 14, 2022

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