Let S be the set S= {a+bk: a,b e 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, х+у:3 (а+с)+ (b+ d)k, ху:%3...

Prove the multiplicative inverse law is false for S.

Let S be the set<br>S= {a+bk: a,b e R},<br>where k is a formal symbol. Define addition and multiplication operations on S as<br>follows: given elements x = a+bk and y =c+dk in S,<br>х+у:3 (а+с)+ (b+ d)k,<br>ху:%3 (ас + bd) + (ad + be)k.<br>

Extracted text: Let S be the set S= {a+bk: a,b e 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, х+у:3 (а+с)+ (b+ d)k, ху:%3 (ас + bd) + (ad + be)k.

Jun 03, 2022

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Let S be the set S= {a+bk: a,b e 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, х+у:3 (а+с)+ (b+ d)k, ху:%3...

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