<prompt> Ka lipolelo tse nè kapa ka tlaase ho moo, hlalosa hore na bopaki ke eng thutong ea lipalo.nan  <response>: Instruction in English: In four sentences or less, explain what a proof is in mathematics. . Response in English: A proof is a logical argument that uses a set of axioms or previously proven statements to demonstrate the truth of a mathematical statement. It works by deriving conclusions from a series of premises or by contradiction, showing that the statement must be true in all possible cases. Proofs provide a rigorous way to establish and verify theorems, which are general facts or principles that can be applied to solve complex problems. A proof must be complete, logically sound, and free from any ambiguity or contradiction to be considered valid in mathematics. . Response in Sesotho: Bopaki ke khang e utloahalang e sebelisang sehlopha sa axioms kapa lipolelo tse pakiloeng pele ho bontša nete ea polelo ea lipalo. E sebetsa ka ho fumana liqeto ho tsoa letotong la libaka kapa ka ho ikhanyetsa, e bontšang hore polelo e tlameha ho ba nete maemong ohle a ka khonehang. Bopaki bo fana ka mokhoa o tiileng oa ho theha le ho netefatsa theorems, e leng lintlha tse akaretsang kapa melao-motheo e ka sebelisoang ho rarolla mathata a rarahaneng. Bopaki bo tlameha ho ba bo felletseng, bo utloahalang, me bo se ke ba e-ba le pherekano leha e le efe kapa likhanyetsano tse lokelang ho nkoa e le tsa bohlokoa thutong ea lipalo. 