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एक समूह (G, ∗) का एक सबसेट H एक समूह है यदि _____ है।

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UP TGT Mathematics 2016 Official Paper
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  1. a, b ∈ H ⇒ a ∗ b ∈ H
  2. a ∈ H ⇒ a-1 ∉  H
  3. a, b ∈ H ⇒ a ∗ b-1 ∈ H
  4. H में समानता तत्व नहीं होता है

Answer (Detailed Solution Below)

Option 3 : a, b ∈ H ⇒ a ∗ b-1 ∈ H
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अवधारणा:

एक समूह (G, ∗) का गैर-रिक्त सबसेट G का एक समूह है यदि,

⇒ a, b ∈ H ⇒ a ∗ b-1 ∈ H

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