<prompt> Netefatsa molao oa kopanelo oa tlatsetso bakeng sa linomoro tsa nete.nan  <response>: Instruction in English: Prove the associative law of addition for real numbers. . Response in English: The associative law of addition for real numbers states that for any real numbers a, b, and c, the order in which you add them does not matter; the result will be the same. In other words, a b c a b c.Proof:Consider three arbitrary real numbers, a, b, and c. According to the definition of real number addition, the sum a b is the unique real number r for which there exists a real number s such that a s b and r s.Similarly, the sum b c is the unique real number t for which there exists a real number u such that b u c and t u.Thus, we have two equations: r c s c and a t a u.By the commutative property of addition for real numbers, s c c s and a u u a. Substituting these in the above equations, we have r c c s and a t u a.Since addition of real numbers is defined to have the property that if x y z and w y z, then x w, we have r c s and t u a.Substituting these back in the original equations, we get a b c a u a and a b c s c c.It is clear that a u a s c c, which means that a b c a b c.Hence, the associative law of addition for real numbers is proven. . Response in Sesotho: Molao oa kopanelo oa tlatsetso bakeng sa linomoro tsa sebele o bolela hore palo efe kapa efe ea sebele a, b, le c, tatellano eo u li kenyang ka eona ha e na taba; sephetho se tla tšoana. Ka mantsoe a mang, a b c a b c. Bopaki: Nahana ka linomoro tsa sebele tse tharo, a, b, le c. Ho latela tlhaloso ea tlatsetso ea nomoro ea nete, kakaretso a b ke nomoro ea nete e ikhethang r eo ho eona ho nang le nomoro ea nete e kang a s b le r s. Ka mokhoa o tsoanang, kakaretso ea b c ke nomoro ea nete e ikhethang t eo ho eona ho nang le nomoro ea sebele ea hore b u c le t u. Kahoo, re na le li-equations tse peli: r c s c le t a u. Ka thepa ea phalliso ea tlatsetso bakeng sa linomoro tsa sebele, s c c s le u u a. Ho beha tsena boemong ba lipalo tse ka holimo, re na le r c c s le t u a. Kaha ho phaella ha linomoro tsa sebele ho hlalosoa ho ba le thepa ea hore haeba x y z le w y z, joale x w, re na le r c s le t u a. Ha re kenya tsena hape ho li-equation tsa pele, re fumana b c a u a le a b c s c c. Ho hlakile hore a u a s c c, ho bolelang hore a b c a b c. Kahoo, molao oa ho kopanya oa ho eketsa linomoro tsa sebele o netefalitsoe. 