For each of the following indexed collections of sets {Ai : i ∈ I}, determine ∪i∈I...

For each of the following indexed collections of sets {Ai : i ∈ I}, determine ∪i∈I Ai, ∩i∈I Ai, and whether or not the collection is pairwise disjoint. Prove your claims.

(a) I is the set of prime numbers and for each p∈I,Ap ={n∈N: p|n}.
(b) I=R≥0 ={r∈R:r≥0} and for each r∈R≥0,Ar ={(x,y)∈R^2 : sqrt(x^2+y^2) =r}

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Colby Messinger answered 1 year ago

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