Power Set of Null Set

What is the number of element(s) in P ( ϕ ) P(\phi) ?


The answer is 1.

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2 solutions

Munem Shahriar
Nov 23, 2017

ϕ \phi is the subset of every set. Hence it is the only element.

ϕ \phi has only one subset which is itself, ϕ \phi .

So, the power set, P ( ϕ ) = { ϕ } P(\phi)= \{\phi\} has 1 element, while the element is ϕ \phi .

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