Sorry a couterexample that its false for IF A is not subset of B and B not subset of C then A is not sub of C

For all sets A, B, and C, Can anyone prove with a counterexample that IF A is not a subset of B and B is not a subset of C then A is not a subset of C is false.Sorry a couterexample that its false for IF A is not subset of B and B not subset of C then A is not sub of C
To show your statement is false we need an example of sets A, B, and C that satisfy the hypotheses but not the conclusion. So we need sets A,B, and C such that A is not a subset of B, B is not a subset of C, but A IS a subset of C.





This is not difficult. Let A={1} and B={2}. Then A isn't a subset of B. We need C such that A is a subset of C but B isn't. One such C is C={1,3}. Other examples exist. There is at least one simpler example that you should try to find.

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