Question: For each set defined below, determine if the set is countable or uncountable and support your answer with a convincing proof. 1. The set of

For each set defined below, determine if the set is countable or uncountable and support your answer with a convincing proof.

1. The set of all stree objects, defined by:

Base object: null is an stree.

Constructor: for any stree objects q1, q2, combine(q1, q2) is an stree.

2. R Q. (R is set of real numbers, Q is set of Rational numbers)

3. The set of all infinite state machines, M = (S, G, q0) where S = N (aka Natural Numbers), and G S S and q0 S are otherwise unrestricted.

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