How many subsets there can be under following conditions?

Question

Normally, set x is considered equal to set y if x={A,B} and y={B,A}. However, for my question let's assume {A,B} = {B,A} is NOT true because of the sequence of their members. We have a set c with n number of unique elements. How many subsets can there be for the set c if:
*{A,B} and {B,A} are not considered equal or same
*Each subset has maximum two elements
*An element is not repeated in the subset

Is there any specific term for above mentioned phenomenon?

Answer 1

If nPr = n! / (n-r)!,
there will be nP0, or 1, subset with no elements, nP1, or n subsets with one element, and nP2, or n(n-1) ordered subsets with two elements. This adds up to n² + 1 ordered subsets with no more than two elements.

This particular function can often be found on calculators that can do statistical calculations, including many common models of scientific calculators and just about all of them that have a factorial function.

Answer 2

Subsets:
The empty set - 1
single element sets - n

double element subsets - n^2 if you consider {A,A} different from {A} otherwise it would be n^2-n. There must also be at least 2 elements in c for there to be any double element subsets

Total n^2+n+1 or n^2+1

For instance if c = {A,B)
then the set of subsets is {φ,{A},{B},{A,A},{B,B},{A,B},{B,A} }

Answer 3

A={a,b} and B={b,c}
If A is not equal to B, and if the ordering matters, they are not sets, but sequences...i dont think u can use set theory anymore.... but i would say 1 since { } is a subset of any set
{ } emptyset