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A subset H of a group (G, ∗) is a group if
1. a, b ∈ H ⇒ a ∗ b ∈ H
2. a ∈ H ⇒ a-1 ∈ H
3. a, b ∈ H ⇒ a ∗ b-1 ∈ H
4. H contains the identity element

1 Answer

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Best answer
Correct Answer - Option 2 : a ∈ H ⇒ a-1 ∈ H

Concept:

A non-empty subset H of a group (G, ∗) is a group of G iff,

a, b ∈ H ⇒ a ∗ b ∈ H

⇒ a ∈ H ⇒ 1/a ∈ H ⇒ a-1 = 1/a 

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