Question

Starting with 2 sets A and B of respective cardinalities a and b, use all operations on sets that you have learnt:
1) to construct sets whose cardinalities are the following
2) to construct word-problems whose solutions require counting the numbers of the sets you first constructed
a) (b+a)(b-a)
b) b^{a+b}
Please, help.

Answer 1

I don't know how to start.

Answer 2

@mathmate

Answer 3

@IrishBoy123

Answer 4

@loser66 Can we start with a list of the operations you've learned?

Answer 5

yes, sir

Answer 6

Whatever you use, I am ok.

Answer 7

sorry @Loser66 i haven't a clue about this kind of stuff :(

Answer 8

If you're vague about this, then I assume you know at least union, intersection, difference, and complement, right?

Answer 9

It's ok, friend, neither I.

Answer 10

yes

Answer 11

Do you know how to find |A\(\cap\)B| in terms of A and B, using the above operators?

Answer 12

yes, I do.
But first off, I need you to define what are set A and B, please

Answer 13

Since the problem has 2 parts, operation and word problem. We can go backward by defining the sets first and then work on it, right?

Answer 14

The same as in your question, i.e. with cardinalities a and b. But we don't use them for now. Is that ok?

Answer 15

Actually, I was planning to use
a+b = |A|+|B|=|A\(\cap\)B|+|A\(\cup\)B|, and similarly a-b, but then it's not a set, which is what the question asks.
Perhaps @ganeshie8 has a better idea.

Answer 16

I have to go for work now. I will be back after work. If you have any idea, please guide me. I will take it later. Much appreciate.

Answer 17

Well never mind...

Answer 18

Are the sets disjoint?

Answer 19

Hold on, I'll post a pic of my work.

Answer 20

@Kainui or @mukushla Question about sets maybe you might be able to help with.