What Are the Results of Adding and Multiplying Sets A and B?

[Unassuming]

Homework Statement

Let A = {-1,2,4,7}
Let B = {-2,-1,1}

Find A+B and A*B. (multiply)

Homework Equations

The Attempt at a Solution

Am I right here?

A+B = {-3,-2,0,1,2,3,5,6,8}

A*B = {-14,-8,-7,-4,-2,-1,1,2,4,7}

 

[Focus]

Sorry this is a bit confusing. I don't think you can add/multiply sets like that. For multiplication you need the cartesian product which is just (a,b) \quad a\in A, b\in B. If you can expand and say what you mean by multiplying and adding sets then I can help a bit more.

 

[HallsofIvy]

There are a number of different ways to define A+ B or A*B for sets. For example, those are often used to mean union and intersection of sets. I think what you are talking about is "z is in A+ B if and only if z= x+ y for some x in A and some y in B" and "z is in A*B if and only if z= xy for some x in A and some y in B." Assuming those are the definitions you are using, yes, what you have is correct.

 

[Unassuming]

Ahh, so if I defined it as multiplication or addition, then that would be valid.

Define A + B = [ a + b : a in A, b in B }

Likewise for A*B. I was confused because it didn't seem natural.