The set ${2, 4, 16, 256, . . . .}$ can be represented as which one of the following?

{x \in N | x = 2^{2^{n}}, n \in N}

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{x \in N | x = 2^{2^{n}}, n = 0, 1, 2, . . . .}

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{x \in N | x = 2^{2 \cdot n}, n = 0, 1, 2, . . . .}

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{x \in N | x = 2^{4 \cdot n}, n = 0, 1, 2, . . . .}

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Solution

The correct option is C ${x \in N | x = 2^{2^{n}}, n = 0, 1, 2, . . . .}$
Since, ${2, 4, 16, 256...} = {2, 2^{2}, 2^{4}, 2^{8} . . .}$

$\Rightarrow {2^{2^{0}}, 2^{2^{1}}, 2^{2^{2}}, 2^{2^{3}} . . .} \Rightarrow {x ϵ N, x = 2^{2^{n}}, n ϵ W}$

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