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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help with logical statement

**Physics Forums | Science Articles, Homework Help, Discussion**