<prompt> Etsa bopaki ba theorem e latelang:Theorem: Kakaretso ea linomoro tse peli tse sa tloaelehang li lekana.  <response>: Instruction in English: Construct a proof of the following theorem: . Response in English: Statement: The sum of two odd numbers is even.Proof: Suppose we have two odd numbers, a and b. By the definition of an odd number, these numbers can be expressed in the form:a 2m 1,b 2n 1,where m and n are integers.Now consider the sum of these two numbers, which well call C:C a b,Substituting in the respective expressions for a and b, we get:C 2m 1 2n 1,Simplifying this expression, we get:C 2m 2n 2,orC 2m n 1Notice that the expression m n 1 is itself an integer, so we can let k m n 1, and rewrite our expression for C as:C 2kThis is the definition of an even number. Hence we have shown that the sum of two odd numbers is an even number.Thus, the theorem is proved. . Response in Sesotho: Polelo: Kakaretso ea linomoro tse peli tse sa tloaelehang li lekana. Bopaki: Ha re re re na le linomoro tse peli tse sa tloaelehang, a le b. Ho ea ka tlhaloso ea palo e sa tloaelehang, linomoro tsena li ka hlalosoa ka mokhoa: a 2m 1, b 2n 1, moo m le n e leng linomoro. Joale aku nahane ka kakaretso ea linomoro tsena tse peli, tseo re tla li bitsa C: C a b, Ho fetola lipolelong tse fapaneng bakeng sa a le b, re fumana: C 2m 1 2n 1, Ho nolofatsa. polelo ena, re e fumana: C 2m 2n 2, kapa C 2m n 1 Hlokomela hore poleloana m n 1 ka boeona ke palo e feletseng, kahoo re ka lumella k m n 1, me u ngole polelo ea rona ea C hape ka hore: C 2k Ena ke tlhaloso ea palo e lekanang. Kahoo re bontsitse hore kakaretso ea linomoro tse peli tse odd ke palo e lekanang. Kahoo, theorem e pakoa. 