Teaching UP B.Ed (Paper 1 & 2) Mock Test 2025 Engineering Mathematics Set Theory & Algebra

समूह (G, o) से समूह (G', ∗) में परिभाषित फलन f, G से G' में समूह समाकारिता है, यदि :

1
f(a ∗ b) = f(a) o f(b) ∀ a, b ∈ G
2
f(a o b) = f(a) ∗ f(b) ∀ a, b ∈ G
3
f-1(a ∗ b) = f-1(a) o f-1(b) ∀ a, b ∈ G
4
f(a o b) = f(a) ∗ f-1(b) ∀ a, b ∈ G
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