Addition of Families of Intervals, Real Analysis

[jacobsh47]

The question is:
Let A= { [-2,5] , [1/2,2] } and B={ [1,7] , [1/4,3] }. Calculate the family A+B.

Referring to addition of intervals my text says:
Given F and G families of intervals, F+G is the family {I+J where I is in F, J is in G}

I don't understand how to calculate A+B from what the text says. How do you know which intervals in the families to add? Do I add each interval to each other to get 4 intervals in the family? I'm confused.

 

[pka]

The question is:
Let A= { [-2,5] , [1/2,2] } and B={ [1,7] , [1/4,3] }. Calculate the family A+B.

Referring to addition of intervals my text says:
Given F and G families of intervals, F+G is the family {I+J where I is in F, J is in G}

I don't understand how to calculate A+B from what the text says. How do you know which intervals in the families to add? Do I add each interval to each other to get 4 intervals in the family? I'm confused.

How does the text define the addition of intervals as in "I+J"?

 

[jacobsh47]

The text says that I+J is the interval [r+u, s+v]. I also says that I+J is the smallest interval containing all x+y with x in I and y in J.
I feel like I should get how to solve this problem now, but I can't quite get there. Is the answer going to be one interval, or multiple intervals? I am still confused.

 

[daon]

You will have four calculations to do, i.e. A+B will contain for elements, one for each pairing from A to B.

I'll do the first one:

[-2,5] + [1,7] = [-1,12]; its that easy. By "smallest" its meant that if x belongs to [-2,5] and y to [1,7] then s=x+y belongs to S=[-1,12], and if x+y belongs to any other set S' for all x,y then S is a subset of S'.