To'g'rilash uchun rahmat, LaTeX yordamida isbot quyidagicha: $x$ va $y$ ikkita tasodifiy butun son bo'lsin. $xy$ ko'paytmasi agar va faqat agar $x$ va $y$ ikkalasi ham toq bo'lsa, toq bo'ladi. $x$ juft bo'lish ehtimoli $\frac{1}{2}$ va $x$ juft bo'lish ehtimoli ham $\frac{1}{2}$. Xuddi shunday fikrlash orqali $y$ juft bo'lish ehtimoli $\frac{1}{2}$ va $y$ juft bo'lish ehtimoli $\frac{1}{2}$. $xy$ juft bo'lish ehtimoli: $\frac{1}{2}{2}{1}{1
spam fails_task lang_mismatch pii not_appropriate hate_speech sexual_content quality toxicity humor helpfulness creativity violence