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Let A, B and C be sets.

Prove that if A[itex]\subseteq[/itex]B[itex]\cup[/itex]C and A[itex]\cap[/itex]B=∅, then A[itex]\subseteq[/itex]C.

My attempted solution:

Assume A[itex]\subseteq[/itex]B[itex]\cup[/itex]C and A[itex]\cap[/itex]B=∅.

Then [itex]\vee[/itex]x (x[itex]\in[/itex]A[itex]\rightarrow[/itex]x[itex]\in[/itex]B[itex]\cup[/itex]x[itex]\in[/itex]c).

I'm not sure where to start and how to prove this. Any help would be greatly appreciated. Thank you.

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# Let A, B and C be sets. Prove that

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