Let S be the set S= {a+bk : a,b ER}, 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 :=...

a) prove by identity. include a short explanation of how you know what the indemnity elements are. b) prove that the multiplicative inverse law is false for s. (don’t just write down a counter example; also prove that your counter example is valid)

Extracted text: Let S be the set S= {a+bk : a,b ER}, 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+bc)k.