 with error \(\lt \bfrac{1}{4}\). We can then determine whether \(z \gt \bfrac{1}{4}\), in which case \(\sigma \gt 0\), or \(z \lt \bfrac{3}{4}\), when \(\sigma \lt 1\). In the first case, there exists \(x \in S\) with \(x \gt 0\), so we must have \(x = 1\) and therefore \(P\). In the case \(\sigma \lt 1\), we have \(\neg P\). Thus (B) implies the law of excluded middle.