To submit Let S be the set S= {a+bk : a,b € R}, where k is a formal symbol. Define addition and multiplication operations on S as follows: given elements x = a+bk and y =c+dk in S. x+y:= (a+c)+(b+d)k,...

please send handwritten solution for part a


Extracted text: To submit Let S be the set S= {a+bk : a,b € R}, where k is a formal symbol. Define addition and multiplication operations on S as follows: given elements x = a+bk and y =c+dk in S. x+y:= (a+c)+(b+d)k, xy:= (ac +bd) +(ad +be)k. (a) Prove both identity laws for S. Include a short explanation (one sentence is fine) of how you know what the identity elements are (b) Prove that the multiplicative inverse law is false for S. [That is, don't just write down a counterexample; also prove that your counterexample is valid.]