A set is defined recursively as follows:
1. Basis step: 2∈S2∈S2 \in S
2. Recursive step: if x∈Sx∈Sx \in S, then (x+1)∈S(x+1)∈S(x+1) \in S.
Which of the following is the best statement that describes SSS?

Question

A set is defined recursively as follows:

1. Basis step: 2∈S2∈S2 \in S

2. Recursive step: if x∈Sx∈Sx \in S, then (x+1)∈S(x+1)∈S(x+1) \in S.

Which of the following is the best statement that describes SSS?

Answer

Z + ⊂ S Z + ⊂ S Z^+ \subset S

Answer

Z + ⊆ S Z + ⊆ S Z^+ \subseteq S

Answer

S ⊂ Z + S ⊂ Z + S \subset Z^+

Answer

S ⊆ Z + S ⊆ Z + S \subseteq Z^+

Answer

S = Z + S = Z + S = Z^+

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