I am struggling with summation notation! I am attempting to perform the statements that are in bold.
$$\ A = \text{{0, 1, 2, 3, 4}} $$ $$\ B = \text{{3, 5}} $$ $$\ C = \left\{(i, j) : i \in A, j \in B, i + j =3 \right\}$$ $$\ D = \left\{ \left\{i,j \right\} : i \in A, j \in B, i+j = 3 \right\} $$
List all the elements of C
I understand that:
(i, j) is a tuple (or ordered set)
(i,j) "such that" ... i is an element of A, j is an element of B
What I don't understand:
Is this an ordered set, nested inside an unordered set?
would the output be in (i1, j1), (i2, j2) format?
not sure what to do with the i+j=3 portion of the statement?
List all the elements of D
I understand:
{i, j} is an unordered set.
What I don't understand:
Does (i,j) versus {i,j} make any significant changes?
Would the output be similar to that of C?
Any help is greatly appreciated. Thanks!
Yes. Each element of $C$ looks like $(a, b)$.
What's an "output"? You're just asked to list some elements, so give this list in whatever your preferred way of giving a list is. Use bullet points or whatever. There's nothing formal and set-notational going on here.
Almost. It means that $C = \{(0,3)\}$. (This is set notation!) Alternatively, here is a list of all the elements in $C$, using bullet points because that's how I like to list things:
and that's it.
In this case, no. Can you think of examples where it might? What would happen if $A = B = \{0,1,2,3,4\}$, for example?