Multiple choice

The set (1, 2, 3, 5, 7, 8, 9) under multiplication modulo 10 is not a group. Given below are four plausible 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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C Correct answer
Explanation

The definition of binary operation multiplication modulo 10 is a follows aob = (a x b)% 10 And the identity element for the given set = 1 For closure property, 2 or 7 = 4 $\notin$ set So, the set is not closed Here, 2 and 8 do not have an inverse, so 307 = 1 Hence, 7 is the inverse of 3.

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