Hello,

My teacher has given me a problem to try:

Let A={1, 2, 3, 4}. Define a fcn f: Powerset(A) --> N U {0} by f(x) = |x| (cardinality of x) for x element of Powerset(A).

I need to find:

a) f({∅, {1,2}, {2,3}})

b) ƒ−1({3}).

Now, for a, im pretty sure it's simply f({∅, {1,2}, {2,3}}) = 2, since there is nor curly brackets around ∅, so it doesnt count as an element, and other two are elements of powerset (A).

Regarding b, im not too sure what would be the inverse of the cardinality.

For a, is my logic makes sense or i am completely off?

For b, im not sure how to find the inverse.

Thank you for help in advance