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Q: किसी समूह (G, *) का उपसमुच्चय H एक समूह होगा, यदि और केवल यदि–
  • A. a, b ∈ H ⇒ a*b ∈ H
  • B. a ∈ H ⇒ a⁻¹∈H
  • C. a, b ∈ H ⇒ a*b–1∈H
  • D. H में इकाई अवयव है
Correct Answer: Option A - A non empty subset H of a group (G,*) is said to be a subgroup of G if the composition if G induces a composition in H and if H is a group for the induced composition. i.e. subset H is called subgroup of (G,*) if (H,*) is also a group. Let a, b ∈H ⇒ a*b∈H ∀ a,b ∈H
A. A non empty subset H of a group (G,*) is said to be a subgroup of G if the composition if G induces a composition in H and if H is a group for the induced composition. i.e. subset H is called subgroup of (G,*) if (H,*) is also a group. Let a, b ∈H ⇒ a*b∈H ∀ a,b ∈H

Explanations:

A non empty subset H of a group (G,*) is said to be a subgroup of G if the composition if G induces a composition in H and if H is a group for the induced composition. i.e. subset H is called subgroup of (G,*) if (H,*) is also a group. Let a, b ∈H ⇒ a*b∈H ∀ a,b ∈H