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Question

Which of the following is a subgroup of the group G={2n|nZ} under multiplication?

A
{5n|nN}
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B
{3n|nZ}
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C
{6n|nN}
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D
{4n|nZ}
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Solution

The correct option is C {4n|nZ}
The variable Z means an integer value (negative as well positive integer)
and n belongs to Z, this means that the power of 2 can either be negative or positive integer.
22=4
22=14
24=16
24=116

Similarly, for a value 4n can be written as 22n
when n=2
so 42=16
so 22×2=24=16

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