Am I understanding this relation?

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In summary, the conversation discusses a relation T defined on a set of strings made up of a's and b's. The relation is defined as t = as, meaning t is the concatenation of a with s. The question is asked whether certain pairs of strings are related under T or T-1, and the conversation provides explanations and clarifications about the rules of the relation.
  • #1
mr_coffee
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Hello everyone I'm not sure if I'm understanidng this relation.

The question is:

Let S be the set of all strings in a's and b's. Define a relation T on S as folows:

FOr all s, t in S, s T t if and only if t = as. That is, t is the concatenation of a with s.

c. Is ba T aba?
I said yes, because aba is the concatneation of a with ba. Thus a + (ba)

e. Is abb T^-1 bba?

Well I know this means,
(abb T^-1 bba) if and only if (bba T abb)

now abb, can be broken into a + bb, but would that break the rules? like the order odes it have to be the same? So for this one i would say no.



f. Is abba T^-1 bba?

this means
bba T abba
I would say yes, becuase
abba is just a + bba


Any clarification if I'm understanding right?

Thanks!
 
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  • #2
mr_coffee said:
Hello everyone I'm not sure if I'm understanidng this relation.

The question is:

Let S be the set of all strings in a's and b's. Define a relation T on S as folows:

FOr all s, t in S, s T t if and only if t = as. That is, t is the concatenation of a with s.

c. Is ba T aba?
I said yes, because aba is the concatneation of a with ba. Thus a + (ba)
Good!

e. Is abb T^-1 bba?

Well I know this means,
(abb T^-1 bba) if and only if (bba T abb)
Yes, that's correct. T-1 is just T reversed. s T-1 t if and only if s is at. abbT-1bba is NOT true because bbaTabb is not true.

now abb, can be broken into a + bb, but would that break the rules? like the order odes it have to be the same? So for this one i would say no.
Yes, of course. The same letters in different order are different strings. Nothing in the definition of T or T-1 changes that!



f. Is abba T^-1 bba?

this means
bba T abba
I would say yes, becuase
abba is just a + bba
Good!

Any clarification if I'm understanding right?

Thanks!
 
  • #3
thanks for the help!
 

What is a relation?

A relation is a pairing or connection between two sets of data, where the elements in one set are related to elements in the other set in some way.

What is the purpose of understanding a relation?

Understanding a relation can help us make sense of the connections between different sets of data and can provide valuable insights and information about these connections.

What are some common types of relations?

Some common types of relations include functional relations, where each element in one set corresponds to exactly one element in the other set; one-to-one relations, where each element in one set corresponds to exactly one element in the other set and vice versa; and many-to-one relations, where multiple elements in one set can correspond to a single element in the other set.

How can I determine if I am understanding a relation correctly?

One way to determine if you are understanding a relation correctly is to use visual aids, such as graphs or diagrams, to help visualize the connections between the two sets of data. You can also check your understanding by explaining the relation to someone else or by solving problems related to the relation.

What are some real-world examples of relations?

Real-world examples of relations can include the relationship between a person's height and weight, the relationship between a company's profit and expenses, and the relationship between the distance traveled and the time it takes to travel that distance. Relations can also be found in mathematical equations, such as y = x^2, where y is related to x by squaring the value of x.

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