I am writing a theorem to do with a fractional factorial design for an experiment. I have had minimal formal training in mathematics, and this is my first theorem. I am fairly happy with most of the statement, but the last part does not feel right.(adsbygoogle = window.adsbygoogle || []).push({});

Basically I want to say "If S is a subset of R, where the cardinal number of S is less than n(l-1)+1, then out of all possible sets composed of symmetric differences and unions (of the symmetric differences) between elements of S there does not exist a superset of P.

S⊂R:|S|<n(l-1)+1 ⇒∀{α│s_{x}∆s_{y}∧s_{x}∪s_{y}:(s_{x}∧s_{y})∈S∨(s_{x}∧s_{y})=s_{x }∆s_{y}}∄α⊃P

Note: This is not the full theorem, I have defined n, l, R and P in a previous statement.

Can anyone confirm if this is correct, and if it isn't how I can correct it?

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# Help with logical statement

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