Solving a Homework Problem Involving S={0,1,2,3,4,5,6}

[sportlover36]

Homework problem stated this:

Let S={0,1,2,3,4,5,6}
let * be defined by x*y=max(x-y,0)

is it commutative, associative, does it have an identity and inverse? help please!

I put that yes it is commutative and yes for associative, but I'm not to sure they are right becuase the 6 is throwing me off

for identity i got x*e=x and e*x=x
x+e=x e+x=x
e=0 e=0
so yes it has and identity element of zeero and then i pluged it into x*b=e and b (inverse) came out to be equal to x but idk what to do with the 6!

please help!

 

[Dick]

I don't think you are really dealing with the definition of '*' very well. Do an exercise first. What is 3*2 and what is 2*3? Use the definition of '*'.

 

[sportlover36]

ohsorry! i meant x*y=min(x+y,6)

 

[sportlover36]

I don't think you are really dealing with the definition of '*' very well. Do an exercise first. What is 3*2 and what is 2*3? Use the definition of '*'.

ohsorry! i meant x*y=min(x+y,6)

 

[Dick]

ohsorry! i meant x*y=min(x+y,6)

Well, that makes a difference. But now I'm not sure what part is actually confusing you. Sure, 0 is AN identity. As for inverses, what would be the inverse of 1?

 

[sportlover36]

Well, that makes a difference. But now I'm not sure what part is actually confusing you. Sure, 0 is AN identity. As for inverses, what would be the inverse of 1?

whats confusing me is the 6 in min(x+y , 6). And I am not sure how to find the inverse property using the identity element

were the first 3 right?

 

[Dick]

whats confusing me is the 6 in min(x+y , 6). And I am not sure how to find the inverse property using the identity element

were the first 3 right?

Yes, I think the first three are right. I don't see why the '6' is confusing you. min(x+y,6) is the minimum of the number x+y and the number 6. Yes, the identity is 0. So if x is an inverse of 1 then it must satisfy x*1=0. Is there such an x?

 

[sportlover36]

Yes, I think the first three are right. I don't see why the '6' is confusing you. min(x+y,6) is the minimum of the number x+y and the number 6. Yes, the identity is 0. So if x is an inverse of 1 then it must satisfy x*1=0. Is there such an x?

umm well x times 0 equals 0 but if we are saying x*1 as the operation then the only one after plugging it into x+y=0 is -1

i don't know if that made sense

 

[Dick]

umm well x times 0 equals 0 but if we are saying x*1 as the operation then the only one after plugging it into x+y=0 is -1

i don't know if that made sense

It makes sense, but -1 isn't in S={0,1,2,3,4,5,6}. If there is an inverse, you need it to be a member of S.

 

[sportlover36]

It makes sense, but -1 isn't in S={0,1,2,3,4,5,6}. If there is an inverse, you need it to be a member of S.

so there is no inverse since it does not exist in the S!

 

[Dick]

so there is no inverse since it does not exist in the S!

Exactly.

 

[sportlover36]

Exactly.

Thank you soooo much for your help and time!