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The set $\{1,2,3,5,7,8,9\}$ under multiplication modulo $10$ is not a group. Given below are four possible reasons. Which one of them is false?

  1. It is not closed
  2. $2$ does not have an inverse
  3. $3$ does not have an inverse
  4. $8$ does not have an inverse

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Best answer
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Answer: C

$3$ has an inverse, which is $7.$
$3*7 \mod 10 = 1.$
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Ans C.
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Hi , please correct me if I am wrong. The set is {1,2,3,5,7,8,9} and we need to do multiplication modulo 10.  So, 2 (multiplication modulo 10 ) 2 = 4 , which is not in the set. That means , it is not closed.

Please correct me , if I am wrong .
Answer:

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