Let's prove that, if a set has size \(n\), then that same set has exactly \(2^n\) subsets.
⎕←⎕ucs 2∘⊥∘⌽¨ ↓7 (⊢⍴⍨⊣,⍨÷⍨∘≢) ⍎¨ '0001011001011100101110000111110', '0111010111011110101111010101101', '1100001100101110001011110011100', '0011100001110111010110001111110111011011'