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How do you describe, using set notation, a certain set of n-tuples generated from a set satisfying the following conditions

Condition 1: non of the components of an individual n-tuple can equal each other

Condition 2: if (a,b) is an element of the set then (b,a) can not be an element of the set as well, I believe this is called not being symmetric

I believe the above conditions are analogous to generating all unique n-element subsets from a set, except I need to convert to n-tuple form

For instance, I have a set A = {S1, S2, S3, S4, DS1, DS2}, I would like to describe the set consisting of all the following 2-tuples generated from A, using set notation.

That is, describe the set below using set notation

S = {(S1,S2), (S1, S3), (S1, S4),(S1, DS1), (S1, DS2), (S2, S3), (S2, S4),

(S2, DS1), (S2, DS2), (S3, S4), (S3, DS1), (S3, DS2), (S4,DS1), (S4, DS2), (DS1, DS2)}

This is my best attempt

S= {(x1 , x2): {x1 , x2} [tex]\subseteq[/tex] A}

I'm assuming that by stating ({x1 , x2} [tex]\subseteq[/tex] A) that alone guarantees generation of all unique subsets which satisfy the conditions above, where the x1 , x2 of each generated subset are assigned to the x1 , x2 values of the 2-tuple

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# Describing all unique 2-tuples from a set using Set Notation

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