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KCET2012MathematicsMathematical Reasoning

Which of the following is a subgroup of the group G= 2^ n n Z under multiplication?

Options

  1. A4^ n n N
  2. B3^ n n Z
  3. C6^ n n N
  4. D4^ n n Z

Correct answer

D. 4^ n n Z

Step-by-step solution

Since, 4^ n n N , 3^ n n Z and 6^ n n N are not subset of the group G = 2^ n n Z and not satisfy all the properties of group axiom but 4^ n n Z is a subset of G = 2^ n n Z and satisfy all the properties, i.e., closure, associative, multiplicative inverse, multiplicative identity exist with respect to multiplication. So, 4^ n n Z is a subgroup.

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