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GATE20004
+14
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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.
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asked
Sep 14, 2014
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Set Theory & Algebra
by
Kathleen
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edited
Jun 21, 2017
by
Silpa

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1
Answer
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Best answer
A
$1$ is the identity element. Inverse does not exist for zero. So, it is not a group.
answered
Jun 26, 2015
by
Anu
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5.9k
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edited
Dec 17, 2017
by
pavan singh
comment
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Then how can A be a group?
0
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?
+1
Sorry. i misread the question and didn't see the A, B separation in answer.
+1
it's ok :)
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