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+14 votes
Let $S= \{0, 1, 2, 3, 4, 5, 6, 7\}$ and $⊗$ denote multiplication modulo $8,$ that is, $x ⊗ y= (xy) \mod 8$

Prove that $( \{ 0, 1\}, ⊗)$ is not a group.

Write three distinct groups $(G, ⊗)$ where $G ⊂ S$ and $G$ has $2$ elements.
asked in Set Theory & Algebra by Veteran (59.5k points)
edited by | 578 views

1 Answer

+14 votes
Best answer

A $1$ is the identity element. Inverse does not exist for zero. So, it is not a group.

answered by Loyal (5.9k points)
edited by
Then how can A be a group?
Sorry I can't get your question.Actual question is to prove A is not a group.I also proved it.Is there is any mistake?
Sorry. i misread the question and didn't see the A, B separation in answer.
it's ok :)

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