Let A, B and C be three events such that P(C)=0

Statement-1: $(A ∩ B ∩ C) = 0$

Statement-2:$(A ∩ B ∩ C) = P(A ∪ B)$

Statement 1 is True, Statement 2 is True; Statement 2 is not a correct explanation for Statement 1.

We know that

$A ∩ B ∩ C ⊆ C$

$∴ P(A ∩ B ∩ C) ≤ P(C)=0 ⇒ P(A ∩ B ∩ C) =0$

So, statement-1 is true.

Similarly, $ A ∩ C ⊆ C$ and $ B ∩ C ⊆ C$

$⇒ P(A  ∩ C) =0 $ and $P(B  ∩ C)=0$

$∴ P(A ∪ B∪C)=P(A) +P(B) +P(C) -P(A ∩B) -P(B ∩ C) -P ( C∩A)+P(A ∩ B ∩ C)$

$⇒P(A ∪ B∪C)=P(A) +P(B) +0 - P(A ∩ B) -0-0 +0$

$⇒P(A ∪ B∪C)=P(A) +P(B) +P(A ∩ B) = P(A ∩ B)$

So, statement-2 is true.