Prove That (A ∪ B) − B = A − B
Question:
For any two sets \( A \) and \( B \), prove that:
\[ (A\cup B)-B=A-B \]Solution
\[ (A\cup B)-B \] \[ =(A\cup B)\cap B’ \] \[ =(A\cap B’)\cup(B\cap B’) \] \[ =(A\cap B’)\cup\phi \] \[ =A\cap B’ \] \[ =A-B \]Hence proved.