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.