If A = B and B ⊆ C, is A ⊆ C?

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Multiple Choice

If A = B and B ⊆ C, is A ⊆ C?

When two sets are equal, they contain exactly the same elements. If B is a subset of C, every element of B is in C. Since A and B are the same set, every element of A is also in C. That makes A a subset of C. This also uses the idea that equality gives A ⊆ B and B ⊆ A, and the subset relation is transitive: if A ⊆ B and B ⊆ C, then A ⊆ C. So the statement is true, and A ⊆ C holds.

When two sets are equal, they contain exactly the same elements. If B is a subset of C, every element of B is in C. Since A and B are the same set, every element of A is also in C. That makes A a subset of C. This also uses the idea that equality gives A ⊆ B and B ⊆ A, and the subset relation is transitive: if A ⊆ B and B ⊆ C, then A ⊆ C. So the statement is true, and A ⊆ C holds.

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