Proof that (P(A) △ P(B)) ∩ P(A △ B) = ∅ and A = B are Equivalent

In this exercise we will proof that (P(A) △ P(B)) ∩ P(A △ B) = ∅ is equivalent to A equals B. The triangle means the symmetric difference and P is the power set. In this video we will use the proof by contradiction to proof it.

⏰ Timeline 00:00 Exercise 00:05 ⇒ Implication from left to right 04:24 ⇐ Implication from right to left

🔢 Statement to proof (P(A) △ P(B)) ∩ P(A △ B) = ∅ ⇔ A = B

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