Combinations of 2 sets

[saifshk17]

I am having difficulty intersecting two different sets. The first set is formatted structured set while the second set is unstructured. That is values can interchange positions with each other in second set. I will explain with an example:

First Set:
[(1..5,1..12)]

Second Set:
[(A..Z,0..9,0..9)]

The second set can have 3 sets such as:
[(A..Z,0..9,0..9)],[(0..9,A..Z,0..9)],[(0..9,0..9,A..Z)]

So an intersection example of First set and Second set would be a total of 5 placement of values
Examples:

[(1,5),(A,2,9)],
[(1,5),(A,2,9)],
[(3,11),(8,T,9)],
[(3,11),(8,T,9)],
[(4,12),(9,2,P)],
[(4,12),(9,2,P)],
[(1,2),(A,1,0)],
[(1,2),(A,1,0)],
[(5,10),(F,2,9)],
[(5,10),(F,2,9)],
[(5,7),(3,A,3)],

So my question is how many number of sets can be generated with intersection of structured 1st set and unstructured 2nd set?

 

[Dr.Peterson]

Please define the sets in words. I may be misinterpreting your symbolism.

But it appears that the first set is a set of ordered pairs, while the second is a set of ordered triples. The intersection is empty, because nothing is both a pair and a triple!

Maybe you mean the Cartesian product?

 

[saifshk17]

Please define the sets in words. I may be misinterpreting your symbolism.

But it appears that the first set is a set of ordered pairs, while the second is a set of ordered triples. The intersection is empty, because nothing is both a pair and a triple!

Maybe you mean the Cartesian product?

The first set is ordered but second set is not ordered. And its more like intersection of these two sets to combine into one set

 

[pka]

I would like to know from what textbook this question comes?
The notation is so non-standard as to make the statements meaningless to most readers.
I think the we need to see the complete set of definitions.

 

[Dr.Peterson]

The first set is ordered but second set is not ordered. And its more like intersection of these two sets to combine into one set

You'll have to explain at length what you mean, since you are using non-standard terms. You are absolutely not talking about an "intersection"; and a "set" can't be ordered. I think you mean that the elements of the first set are ordered pairs; but I think the second set consists of ordered triples, though any one of the three items in a triple may be a letter. I imagine that you do distinguish (A,2,9) from (2,A,9).

But the hardest part is to figure out what you mean by "combine into one set". Probably if you tell us the context of the question, how it was originally stated, and how the answer is to be used, we may begin to understand.

 

[HallsofIvy]

"
First Set:
[(1..5,1..12)]

That is very peculiar notation. Do you mean "ordered pairs in which the first is an integer from to 5 and tbe second is ab integer from 1 to 12"? If so, the standard notation would be something like \(\displaystyle \{(x, y)| 1\le x\le 5, 1\le y\le 12}\).

Second Set:
[(A..Z,0..9,0..9)]

And this is "the set of ordered triples in which the first is a capital letter and the second and third are integers from 1 to 9?

And you are asking for their intersection? That's the empty set because the two sets have NOTHING in common! The first consists only of pairs and the second only of triples.

The second set can have 3 sets such as:
[(A..Z,0..9,0..9)],[(0..9,A..Z,0..9)],[(0..9,0..9,A..Z)]

I don't know what it means for a set to "have 3 sets".