Prove That If A ⊂ B Then C − B ⊂ C − A
Question:
If \( A \), \( B \), \( C \) are three sets such that \( A\subset B \), then prove that:
\[ C-B\subset C-A \]Solution
Let \( x\in C-B \).
\[ x\in C \quad \text{and} \quad x\notin B \]Since \( A\subset B \),
\[ x\notin B \Rightarrow x\notin A \]Therefore,
\[ x\in C \quad \text{and} \quad x\notin A \] \[ x\in C-A \]Hence,
\[ C-B\subset C-A \]Hence proved.