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Power Set

The number of...

Question

The number of elements in the power set of the set ${(a, b) : a^{2} + b^{2} = 7, a, b \in Z}$ is

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Solution

Clearly, $a^{2} + b^{2} \neq 7$ for any $a, b \in Z$
$∴$ Given set has no elements.
Hence, the number of elements in power set $= 2^{0} = 1$

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