I hope that someone can help me with the following problem:
Problem: Proof by induction that (attached as '.jpg'):
Is it true that $\displaystyle A_1\cup A_2=(A_1\setminus A_2)\cup (A_2\setminus A_1)\cup (A_1\cap A_2)?$
Is it true that $\displaystyle A_1\cup A_2 \cup A_3=(A_1\setminus A_2)\cup (A_2\setminus A_3) \cup (A_3\setminus A_1)\cup (A_1\cap A_2 \cap A_3)?$.