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1. The set of all real numbers under the usual multiplication operation is not a group since
multiplication is not a binary operation
multiplication is not associative
identity element does not exist
zero has no inverse
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2. If (G, .) is a group such that (ab)- 1 = a-1b-1, ∀ a, b ∈ G, then G is a/an
commutative semi group
abelian group
non-abelian group
None of these
3. If (G, .) is a group such that a2 = e, ∀a ∈ G, then G is
semi group
none of these
4. The inverse of - i in the multiplicative group, {1, - 1, i , - i} is
1
-1
i
-i
5. The set of integers Z with the binary operation "*" defined as a*b =a +b+ 1 for a, b ∈ Z, is a group. The identity element of this group is
0
12
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