Composition Relation: How to find the {a | aR2} and {b | 2Rb} in relation R

[inshome]

I am currently studying composition relation and I saw this given practice question online but I am not sure what should I do to answer it.

Here is the question:

Let R be the following relations on A = {0,1,2,3,4,5} and R = {(0,0), (1,1), (1,2), (2,2), (2,4), (3,3), (3,5), (4,1), (5,2), (5,4), (5,0)}

Find:
a. X = {a | aR2}
b. Y = {b | 2Rb}

Would the answer be
a. X = {(1,2), (2,2), (5,2)}
b. Y = ((2,2), (2,4)}

Can you clarify if my answer is right? Thank you so much!

 

[Dr.Peterson]

I am currently studying composition relation and I saw this given practice question online but I am not sure what should I do to answer it.

Here is the question:

Let R be the following relations on A = {0,1,2,3,4,5} and R = {(0,0), (1,1), (1,2), (2,2), (2,4), (3,3), (3,5), (4,1), (5,2), (5,4), (5,0)}

Find:
a. X = {a | aR2}
b. Y = {b | 2Rb}

Would the answer be
a. X = {(1,2), (2,2), (5,2)}
b. Y = ((2,2), (2,4)}

Can you clarify if my answer is right? Thank you so much!

You almost have the right idea.

But X is a set of elements of A, not of ordered pairs. So you want to list only the "a" values from those pairs: {1, 2, 5}. This is the set of all elements of A that are related (on the left) to 2 by R.

Y is similar, but on the other side.

I don't see anything about composition here; I suppose that will come later.

 

[inshome]

You almost have the right idea.

But X is a set of elements of A, not of ordered pairs. So you want to list only the "a" values from those pairs: {1, 2, 5}. This is the set of all elements of A that are related (on the left) to 2 by R.

Y is similar, but on the other side.

I don't see anything about composition here; I suppose that will come later.

Thank you for your response. I'll just clarify if I get your comment right. So the question is only asking for the value of a and b? and the answer on a.) would be {1, 2, 5} and in b.) is {2,4}?

 

[Dr.Peterson]

Thank you for your response. I'll just clarify if I get your comment right. So the question is only asking for the value of a and b? and the answer on a.) would be {1, 2, 5} and in b.) is {2,4}?

Yes.

That's what the notation means: {a | aR2} means "the set of all elements a [of A] such that a is related to 2 by R". It would have been a little clearer if they had, as is usually done, specified {a∈A | aR2}. What's before the bar says what sort of thing is in the set, and what follows the bar gives a condition for being in the set.

 

[inshome]

T

Yes.

That's what the notation means: {a | aR2} means "the set of all elements a [of A] such that a is related to 2 by R". It would have been a little clearer if they had, as is usually done, specified {a∈A | aR2}. What's before the bar says what sort of thing is in the set, and what follows the bar gives a condition for being in the set.

Thank you for your help! I now understand.