# Tagged Questions

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### Binary relation, reflexive, symmetric and transitive

I have a question regarding an image. I'm currently studying binary relations and the following image confused me: What got me confused is that the page from which I got the link ...
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### Equivalence Relation with multiples

How can I prove the equivalence of this relation, and how can I calculate the equivalence class of (4,8)? On the set the relation R is definded by (a,b)R(c,d) ⇔ ad=bc. Find out if this is an ...
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### Proving that $aRb \iff a^2-b^2=a-b$ is an equivalence relation

Could you help me with that, I don't know how to prove if the relation is an equivalence and the class of 5? On the set of integers, the relationship is defined by $aRb \iff a^2-b^2=a-b$. Find out ...
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### Giving an equivalence relation that corresponds to set partitions

My question is: Give equivalence relation that corresponds to the partitions A1 = {1,3,5} A2 = {2} A3 = {4,6} of the set A = {1,2,3,4,5,6} I don't know what the format of the relation should be, in ...
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### Is the property reflexive, symmetric, anti-symmetric, transitive, equivalence relation, partially ordered given the relation below?

I'm working on this and I'm supposed to figure out if the following properties apply to the below relations. Properties are: ...
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### equivalence classes of ∼ are left cosets of H in G - my attempt

Let $H$ be a subgroup of G, and define a relation $∼$ on G by the rules that $x∼y$ mean $x^{-1}y\in H$. Show that $∼$ is an equivalence relation and its equivalence classes are the left cosets ...
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### Need help understanding transitive relations

My discrete math professor gave an example stating that the following relation is transitive, reflexive, symmetric, and antisymmetric. A = {a,b,c,d} R = {(a,a), (b,b), (c,c), (d,d)} I do not ...
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### Equivalence relations proof

I need to prove that if $R_1$ and $R_2$ are equivalence relations on the set $A$, then $R_1\cap R_2$ is an equivalence relation. Problem is I dont know how. Please help!
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### Discrete Math Proofs, Partial Orders and Equivalence Relations

I am horribly stuck on $3$ proofs for my discrete math class. Any help would be greatly appreciated. Prove that if $R$ is a partial order, then $R^{-1}$ is a partial order Prove that if $R_1$ and ...
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### Prove a relation is a equivalence

Let $\sim$ be defined so that $a\sim b$ when $a+b$ is even. Is this an equivalence relation? Equivalence relations confuse me a lot, so any help is appreciated!
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### equivalence properties of $\equiv \pmod n$ proofs

Prove the identity: $$a \equiv b \pmod n \wedge a\equiv c \pmod n\implies b\equiv c \pmod n$$ I need to prove this property of $\equiv \pmod{n}$ along with a few others can someone link me to a ...
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### What exactly are equivalence classes

What exactly are equivalence classes? Suppose I have an equivalence relation $\sim$ on some set $X$ we denote this as $x \sim y$. The equivalence classes are then $[x] = \{y \in X : y \sim x\}$. ...
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### Equivalence relation and equivalence class question

Show that the relation $\sim$ defined on the set $X = \mathbb{N} \times \mathbb{N} = \{(a, b) : a \in \mathbb{N}; b \in \mathbb{N}\}$ as $(a,b) \sim (c,d)$ if and only if $a + d = c + b$ is an ...
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### Give an example of a relation R on $A^2$ which is reflexive, symmetric, and not transitive

I am just looking for some clarification on this exercise: Let $A = \{a,b,c,d\}$. Give an example of a relation $R$ on $A^2$ which is reflexive, symmetric, and not transitive. I understand that if I ...
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### How to find the Equivalence class for a given set?

I'm really having trouble understanding these equivalence classes. Could someone please guide me through the following problem step by step, and help explain this. I have a final exam next week, and ...
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### list all the equivalence relation [duplicate]

list all the equivanlance relations in the set A={1,2,3,4) so there should be 15 right? so what I got so far (1 1) (22) (33) (44) (12) (13) (14) (21) (23) (24) (31) (32) (34) (41) (42) (43) these ...
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### Equivalence Relation on R (real numbers)

Let R be the relation on R(real numbers) defined by: For all x, y (that belong) to R(real numbers), x relates y <=> x-y (that belongs) to Z. (a) Is R an equivalence relation? Prove your answer. ...
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### Describing Equivalence Classes using set builder notation

How would you describe all the equivalence classes for the relation: $congruence$ $modulo$ $5$ over $Z$, using set builder notation?
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### Checking the equivalence relations of sets

$S=\{0,1,2,3\}, R:SxS, (m,n)\in R \text{ if } m+n=4$. From the condition of $R$, I found that $R=\{(2,2),(1,3),(3,1)\}$. Now I have to see if $R$ is reflexive, symmetric, antisymmetric, and ...
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### Inference Proof with Quantifiers

I am trying to figure out this implication proof. Can any of you guys tell me how to prove this? Prove ∀x((¬P(x) ∧ Q(x)) → R(x)) Implies ∀x(¬R(x) → P(x))
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