# Thread: Induction Proof Problem (for set union)

1. ## Induction Proof Problem (for set union)

I hope that someone can help me with the following problem:

Problem: Proof by induction that (attached as '.jpg'):

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3. Hi,
I don’t know how to use the induction hypothesis here.

4. Is it true that $A_1\cup A_2=(A_1\setminus A_2)\cup (A_2\setminus A_1)\cup (A_1\cap A_2)?$

Is it true that $A_1\cup A_2 \cup A_3=(A_1\setminus A_2)\cup (A_2\setminus A_3) \cup (A_3\setminus A_1)\cup (A_1\cap A_2 \cap A_3)?$.