Suppose A, B, and C are sets.(adsbygoogle = window.adsbygoogle || []).push({});

Prove that if A union B is a subset of C, then A is a subset of C and B is a subset of C.

My proof:

Suppose A, B, and C are sets such that A union B is a subset of C.

Then for all x, if x is in A union B, then x is in C.

Since x is in A union B, this means x is in A or x is in B.

Then if x is in A or x is in B, then x is in C.

Hence, if x is in A, then x is in C, and if x is in B, then x is in C.

Thus, A is a subset of C and B is a subset of C.

Is this ok?

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# Is this a clear proof?

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