Here is the set: {1,2,{3,4},5}. This is the roster form. How can this Set be written in Set-builder form?
{ x | ( x ∈ ℕ and ( 0 < x < 3 or x = 5 ) ) or ( x ∈ PowerSet(ℕ) and Cardinality(x) = 2 and ∀y∈x ( 2 < y < 5 ) ) }
You may have missed that it is already in set builder notation. If you perforce want the \(\{x \,\mid\, \phi(x) \}\) form then \(\{ x \,\mid \,x \in \{1,2,\{3,4\},5\}\}\) would be an easier way than rpenner's suggestion, but it would be just as silly, since the list form is readily accepted as set builder notation, anyway. Hence, my question: what context do you need this for? Homework? Which grade? Etc.