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Recent questions tagged goclasses_wq7
3
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1
answer
1
GO Classes 2023 | Weekly Quiz 7 | Question: 1
Let $\text{M}(x)$ denote the predicate $x$ is a mobile ; $\text{B}(x)$ denote the predicate $x$ is black ; $\text{C}(x)$ denote the predicate $x$ has calculator . Suppose that the universe is set of all mobiles. Which of the following ... $: \forall x ( \text{M}(x) \wedge \text{C}(x) )$
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goclasses
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first-order-logic
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1-mark
1
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1
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2
GO Classes 2023 | Weekly Quiz 7 | Question: 2
Let the universe be the set of all integers. Which of the following statements is/are true? (Where “$+$” is the integer addition) $\forall x \forall y \exists z (x+y = z)$ $\forall x \exists y \forall z (x+y = z)$ $\exists x \forall y \exists z (x+y = z)$ $\exists z \forall x \exists y (x+y = z)$
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Apr 14
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GO Classes
145
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goclasses_wq7
goclasses
mathematical-logic
first-order-logic
multiple-selects
2-marks
2
votes
2
answers
3
GO Classes 2023 | Weekly Quiz 7 | Question: 3
Let $\text{P}$ be a compound proposition over $4$ propositional variables $: a,b,c,d.$ We know that for $a$ compound proposition over $n$ propositional variables, we have $2^{n}$ ... is true for that row. Let $\text{P}$ be $a \leftrightarrow b$ How many models are there for $\text{P}?$
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Mathematical Logic
Apr 14
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GO Classes
164
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goclasses_wq7
goclasses
numerical-answers
mathematical-logic
propositional-logic
2-marks
3
votes
2
answers
4
GO Classes 2023 | Weekly Quiz 7 | Question: 4
Consider the following statement $\text{S}$ in an universe $\text{U}.$ $\text{S} : \forall x \forall y (x = y)$ What is the maximum cardinality of $\text{U}$ such that $\text{S}$ is true?
GO Classes
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in
Mathematical Logic
Apr 14
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GO Classes
173
views
goclasses_wq7
goclasses
numerical-answers
mathematical-logic
first-order-logic
1-mark
4
votes
1
answer
5
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.
GO Classes
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Set Theory & Algebra
Apr 14
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GO Classes
227
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goclasses_wq7
goclasses
set-theory&algebra
relations
multiple-selects
2-marks
1
vote
1
answer
6
GO Classes 2023 | Weekly Quiz 7 | Question: 6
Consider the following logical inferences : $\text{S1} :$ If I study Discrete Mathematics, then I will study Computer Science. If I study C, then I will study Algorithms. Therefore, If I study Discrete Mathematics or C then I will study ... correct but $\text{S2}$ is a correct inference Both $\text{S1}$ and $\text{S2}$ are not correct inferences
GO Classes
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in
Mathematical Logic
Apr 14
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GO Classes
145
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goclasses_wq7
goclasses
mathematical-logic
propositional-logic
2-marks
3
votes
1
answer
7
GO Classes 2023 | Weekly Quiz 7 | Question: 7
Let $\text{A, B}$ be two non-empty sets such that $\text{P(A)} \subset \text{P(B)},$ where $\text{P(S)}$ denotes Power set of set $\text{S},$ and $\subset$ denotes proper subset . Let $\text{M}$ be the universal set and $\text{A, B}$ are proper subsets ... $\{\text{A} \cap \text{B},\text{A}' \cap \text{B}'\}$
GO Classes
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Set Theory & Algebra
Apr 14
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GO Classes
202
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goclasses_wq7
goclasses
set-theory&algebra
set-theory
multiple-selects
2-marks
1
vote
1
answer
8
GO Classes 2023 | Weekly Quiz 7 | Question: 8
Consider the formula $\exists x \exists y \exists z(\text{R}(x, y) \wedge \text{R}(z, y) \wedge \text{R}(x, z) \wedge \neg \text{R}(z, x)).$ For which of the following interpretations, is this formula true? $(\text{N}$ ... $\text{R}(x,y) : y = x0 \;\text{or}\; y = x1.$
GO Classes
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in
Mathematical Logic
Apr 14
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GO Classes
132
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goclasses_wq7
goclasses
mathematical-logic
first-order-logic
multiple-selects
2-marks
3
votes
1
answer
9
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 $\text{A}.$
GO Classes
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Set Theory & Algebra
Apr 14
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GO Classes
145
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goclasses_wq7
goclasses
set-theory&algebra
set-theory
relations
multiple-selects
2-marks
3
votes
1
answer
10
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 $\text{R}?$
GO Classes
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Set Theory & Algebra
Apr 14
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GO Classes
157
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goclasses_wq7
goclasses
numerical-answers
set-theory&algebra
set-theory
relations
1-mark
2
votes
1
answer
11
GO Classes 2023 | Weekly Quiz 7 | Question: 11
Let $\text{A}$ be a non-empty set. Let $\text{P(A)}$ denote the power set of $\text{A}.$ Which of the following is/are necessarily true ? If $x \in \text{A}$ then $x$ cannot be an element of $\text{P(A)}.$ If every element of $\text{P(A)}$ ... $\text{B},$ then $\text{A} \subseteq \text{B}.$ $\text{A} \subseteq \text{P(A)}$
GO Classes
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in
Set Theory & Algebra
Apr 14
by
GO Classes
175
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goclasses_wq7
goclasses
set-theory&algebra
set-theory
multiple-selects
2-marks
2
votes
1
answer
12
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?
GO Classes
asked
in
Set Theory & Algebra
Apr 14
by
GO Classes
246
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goclasses_wq7
goclasses
numerical-answers
set-theory&algebra
set-theory
relations
equivalence-class
2-marks
2
votes
1
answer
13
GO Classes 2023 | Weekly Quiz 7 | Question: 13
The binary relation $\text{R} = \{(0, 0),(1, 1)\}$ on set $\text{A} = \{0, 1, 2, 3 \}$ is Reflexive, Not Symmetric, Transitive Not Reflexive, Symmetric, Transitive Reflexive, Symmetric, Not Transitive Reflexive, Not Symmetric, Not Transitive
GO Classes
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Set Theory & Algebra
Apr 14
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GO Classes
112
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goclasses_wq7
goclasses
set-theory&algebra
relations
1-mark
3
votes
1
answer
14
GO Classes 2023 | Weekly Quiz 7 | Question: 14
Let $\text{N}^{+}$ denote the non-zero positive integers. Define a binary relation $\text{R}$ on $\text{N}^{+} \times \text{N}^{+}$ by $(m, n)\text{R}(s, t)$ if $\gcd(m, n) = \gcd(s, t).$ The binary relation $\text{R}$ is Reflexive Symmetric Transitive Not Transitive
GO Classes
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Set Theory & Algebra
Apr 14
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GO Classes
140
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goclasses_wq7
goclasses
set-theory&algebra
relations
multiple-selects
2-marks
2
votes
1
answer
15
GO Classes 2023 | Weekly Quiz 7 | Question: 15
Let $\text{N}^{+}_{2}$ denote the natural numbers greater than or equal to $2.$ Let $m\text{R}n$ if $\gcd(m, n) > 1.$ The binary relation $\text{R}$ on $\text{N}^{+}_{2}$ is Reflexive Symmetric Transitive Not Transitive
GO Classes
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Set Theory & Algebra
Apr 14
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127
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goclasses_wq7
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