Inquiry & Proof

Maria Mota

April 23, 2016

Solo

Theorem 0.9. If A ⊂ B and B ⊂ C, then A ⊂ B.

Proof. Assuming A ⊂ B and B ⊂ C: By definition of subsets: Suppose we choose an elementin A, meaning x ∈ A, and assuming A ⊂ B, then x ∈ B is also true.

By applying the definition of subset again: Suppose we choose an element in B, meaningx ∈ B, and assuming B ⊂ C, then x ∈ C is also true. Since C contains B and B contains Athen that means A ⊂ C.

Therefore, if A ⊂ B and B ⊂ C, then A ⊂ C is true.

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