help with an algebra proof

[javier]

Please help me with these exercise

 

Let A be a set:

 a) show that being equipotent  is an equivalence relation in P(A)

b)For the set A={a,b,c,d},write the partition of P(A) that generates the relation of being equipotent,better said write the equivalence classes

 

[wasab]

How the hell is this algebra? This is discrete math. 

 

A) first you must prove the relation is transitive, reflexive, and symnetric. If you don't know what these are... Well, you better study because you are missing the fundamentals. 

 

B) only do this if the relations is indeed an equivalent relation otherwise there is no point. I am not really sure what equalpotent really means. I assume it means equal? In this case you have to make sure that elements in the powerset satisfy the relationship mRn such that m=n. In such cases the equivalent classes would just be {(a),(b),(c),(d)}

[Guest]

If I remember correctly you have to do something like 

y1-y2 + x1-x2 = distance 

then you match them to see if they’re the same. Otherwise it may be graphed and you have to show they’re at the same Y. 

I don’t recall exactly how to do this.

Do you have a specific problem? That would help solve it & explain what we did and why we did it. Using abcd is less helpful. This is usually used when explaining a formula & any good reference will have at least 1 example. 

3 hours ago, wasab said:

How the hell is this algebra? This is discrete math. 

In the USA, this is a commonly given equation for algebra, geometry & trigonometry. 

[Dash Lambda]

To prove that equipotence (also called equinumerosity) is an equivalence relation, you need to prove that it is reflexive, symmetric, and transitive.

 

-For reflexivity, you need to show that A=A, which just means that an element is equal to itself.

-For symmetry, you need to show that A=B necessitates B=A, in other words that the order doesn't matter.

-For transitivity, you need to show that if A=B and B=C then A=C, in other words you can change the grouping.

 

To find the equivalence classes, you group the elements of a set into their own sets in which all the elements are equal. So, say, if you had the set [1,2,3,4,5] and you gave the equivalence relation that even numbers equal even numbers and odd numbers equal odd numbers, then you would partition it into [1,3,5] and [2,4].

 

3 hours ago, wasab said:

I am not really sure what equipotent really means.

Equipotent means there's a 1:1 mapping, which really just requires that both sets have the same number of elements.

[wasab]

59 minutes ago, Dash Lambda said:

To prove that equipotence (also called equinumerosity) is an equivalence relation, you need to prove that it is reflexive, symmetric, and transitive.

 

-For reflexivity, you need to show that A=A, which just means that an element is equal to itself.

-For symmetry, you need to show that A=B necessitates B=A, in other words that the order doesn't matter.

-For transitivity, you need to show that if A=B and B=C then A=C, in other words you can change the grouping.

 

To find the equivalence classes, you group the elements of a set into their own sets in which all the elements are equal. So, say, if you had the set [1,2,3,4,5] and you gave the equivalence relation that even numbers equal even numbers and odd numbers equal odd numbers, then you would partition it into [1,3,5] and [2,4].

 

Equipotent means there's a 1:1 mapping, which really just requires that both sets have the same number of elements.

I see. But op doesn't mention what the realstionship is so....??? 

[wasab]

1 hour ago, fpo said:

If I remember correctly you have to do something like 

y1-y2 + x1-x2 = distance 

then you match them to see if they’re the same. Otherwise it may be graphed and you have to show they’re at the same Y. 

I don’t recall exactly how to do this.

Do you have a specific problem? That would help solve it & explain what we did and why we did it. Using abcd is less helpful. This is usually used when explaining a formula & any good reference will have at least 1 example. 

In the USA, this is a commonly given equation for algebra, geometry & trigonometry. 

No, it's discerete math, not algebra. The only algebra study in this area, at least in my school, is Boolean algebra which is totally different from x, y and z you learn in high school. 

[Dash Lambda]

14 minutes ago, wasab said:

I see. But OP doesn't mention what the relationship is so....??? 

Yes he does, equipotence. He has to show that equipotence is an equivalence relation and find the equivalence classes for a particular power set under that relation.

 

13 minutes ago, wasab said:

No, it's discerete math, not algebra. The only algebra study in this area, at least in my school, is Boolean algebra which is totally different from x, y and z you learn in high school. 

I'd say it falls within abstract algebra, though I'm not particularly good with the categories.

[Guest]

22 minutes ago, wasab said:

No, it's discerete math, not algebra. The only algebra study in this area, at least in my school, is Boolean algebra which is totally different from x, y and z you learn in high school. 

I meant it’s commonly taught and given as a problem in algebra classes not that it is algebra. Bad phrasing on my part.