Prove or refute $A\subseteq B \wedge B \nsubseteq C \rightarrow A \nsubseteq C$ I have to prove or refute $A\subseteq B \wedge B \nsubseteq C \rightarrow A \nsubseteq C$ My refutation: $A = \\{1\\}, B = \\{1, 2\\}, C = \\{1, 3, 4\\}$. Statement does not apply. Correct?

You are correct that the statement is not true. This is also evident from the following Venn diagram:

![enter image description here](