Define set from given function and a subset. Abstract math

In summary, the function f(t)=(3t, 3t+1) is defined from Z to ZxZ and the subset B={(5m, 5m+1) : m is an element of Z} is given. The task is to determine the inverse of B, denoted by f^-1(B), which is defined as the collection of t's in Z that satisfy the condition f(t) is in B. This set should not mention the function f.
  • #1
beatka6
21
0

Homework Statement


Let f: Z to ZxZ be the function defined f(t)=(3t, 3t+1) . Let B denote the subset of ZxZ defined by B={ (5m, 5m+1) : m is an element of Z}. Determine f^-1(B). This means that you should define set S with a property of S=f^-1(B). In addition, your definition of S should make no mention of the function f.


Homework Equations





The Attempt at a Solution


From what I understand first we have to find f(B), but B is a subset of ZxZ not Z therefore I don't know what to do with this. Please help.
 
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  • #2
f^{-1}(B) is defined as {t[itex]\in[/itex]Z | f(t)[itex]\in[/itex]B}, i.e., the collection of t's such that f(t) is in B.
 
  • #3
It says that it should have no mention of f in the defined set.
 

1. What is a set in abstract math?

A set in abstract math is a collection of distinct objects, called elements, that are grouped together based on a specific criteria or property. These elements can be numbers, letters, or any other type of objects.

2. How is a set defined from a given function?

A set can be defined from a given function by listing all the values that the function outputs for a given input. These values, when grouped together, form a set. For example, if the function f(x) = x^2, then the set can be defined as {1, 4, 9, 16, ...}.

3. What is a subset in abstract math?

A subset in abstract math is a set that contains only elements that are also present in another set, called the superset. In other words, all the elements of a subset must also be elements of the superset.

4. How is a subset determined in abstract math?

A subset can be determined in abstract math by comparing the elements of the two sets. If all the elements of the first set are also present in the second set, then the first set is a subset of the second set. This can be denoted as A ⊆ B, where A is the first set and B is the second set.

5. What is the importance of sets and subsets in abstract math?

Sets and subsets are important in abstract math because they allow us to categorize and organize different types of objects. They also provide a foundation for other mathematical concepts, such as functions, relations, and logic. Sets and subsets also play a crucial role in proving theorems and solving problems in abstract math.

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