Am I understanding this relation?

[mr_coffee]

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!

 

[HallsofIvy]

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!

 

[mr_coffee]

thanks for the help!