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