KCET2012MathematicsMathematical Reasoning
Which of the following is a subgroup of the group G= 2^ n n Z under multiplication?
Options
- A4^ n n N
- B3^ n n Z
- C6^ n n N
- 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.