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Let c={φ,{φ},{{φ}}} what is the power set of the set c.

Sagot :

LammettHashidn

Given C = {φ, {φ}, {{φ}}}, count all the subsets of C :

• { } (empty set)

• {φ}; {{φ}}; {{{φ}}} (all subsets containing only 1 element)

• {φ, {φ}}; {φ, {{φ}}}; {{φ}, {{φ}}} (all subsets containing only 2 elements)

• {φ, {φ}, {{φ}}} (the set C itself)

Then the power set of C is

P(C) = {{ }, {φ}, {{φ}}, {{{φ}}}, {φ, {φ}}, {φ, {{φ}}}, {{φ}, {{φ}}}, {φ, {φ}, {{φ}}}}

In case that answer is unclear because of all those curly braces, we can let φ' = {φ} and φ'' = {{φ}}, and denote the empty set by ∅. Then

C = {φ, φ', φ''}

and

P(C) = {∅, {φ}, {φ'}, {φ''}, {φ, φ'}, {φ, φ''}, {φ', φ''}, {φ, φ', φ''}}

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