I'm not sure about my solution to the following problem and I'd appreciate it if someone could check it.

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Let

be the set of all subsets of

.

a. Which subsets

of

have inverses for

? What are they?

b. Which subsets

of

have inverses for

? What are they?

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Here is my solution:

a.

is the identity of

with respect to

so the only subset

of

with an inverse with respect to

is

, namely itself.

b.

is the identity of

with respect to

so the only subset

of

with an inverse with respect to

is

, namely itself.