GO Classes Set Theory And Algebra Practice Set 1 | Question: 22

Let $A$ be the set of all ordered pairs of integers, that is, $A=Z \times Z$. Define a binary relation $R$ on $A$ as follows: for all $(a, b),(c, d) \in A$,$$(a, b) R(c, ...

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GO Classes asked May 28, 2023

Set Theory & Algebra
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set-theory&algebra
relations
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GO Classes Set Theory And Algebra Practice Set 1 | Question: 6
Let $A$ be any set. Subset Relation on $\mathrm{P}(\mathrm{A})$ is Anti-symmetric?

Let $A$ be any set. Subset Relation on $\mathrm{P}(\mathrm{A})$ is Anti-symmetric?

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GO Classes asked May 28, 2023

Set Theory & Algebra
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descriptive

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 8
Consider the following binary relations on the naturals (non-negative integers). Which ones are reflexive? Symmetric? Anti-symmetric? Transitive? Partial orders? Justify your claims. $A(x, y)$, defined to be true if and only if $y$ ... because eight comes before eighty-one, and $E(8,8)$ is true because eight comes no later than eight.)

Consider the following binary relations on the naturals (non-negative integers). Which ones are reflexive? Symmetric? Anti-symmetric? Transitive? Partial orders? Justify ...

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391 views

GO Classes asked May 28, 2023

Set Theory & Algebra
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set-theory&algebra
relations
partial-order

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1 votes

1 answer

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GO Classes Set Theory And Algebra Practice Set 1 | Question: 10
Are the following relations reflexive, symmetric, transitive, antisymmetric? Explain. Let $R$ be a relation on $\mathbb{Z}$ such that $(a, b) \in R$ iff $b=a$ or $b=-a$. Let $R$ be a relation on $\mathbb{R}$ ... $(a, b) \in R$ iff $a+b$ is a rational number, that is can be represented by a fraction.

Are the following relations reflexive, symmetric, transitive, antisymmetric? Explain.Let $R$ be a relation on $\mathbb{Z}$ such that $(a, b) \in R$ iff $b=a$ or $b=-a$.Le...

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298 views

GO Classes asked May 28, 2023

Set Theory & Algebra
goclasses-practice-set1
set-theory&algebra
relations
partial-order

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