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Theorem 20 (Associative Law). If x, y, z ∈ N, then (x+y)+z = x+(y+z). Proof. (sketch). This follows from Lemma 17, and the identity A ∪ (B ∪ C) = (A ∪ B) ∪ C.Exercise 9. Write up the above proof. (You do not need to prove the identity A ∪ (B ∪ C) = (A ∪ B) ∪ C, since it is part of basic set theory.)
Theorem 20 (Associative Law). If x, y, z ∈ N, then (x+y)+z = x+(y+z). Proof. (sketch). This follows from Lemma 17, and the identity A ∪ (B ∪ C) = (A ∪ B) ∪ C.
Exercise 9. Write up the above proof. (You do not need to prove the identity A ∪ (B ∪ C) = (A ∪ B) ∪ C, since it is part of basic set theory.)
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