A Note All infinite sets cannot be described in the roster form. For example, the · Part 21

n ( A – B) + n ( A ∩ B ) + n ( B – A ) = n ( A – B) + n ( A ∩ B ) + n ( B – A ) + n ( A ∩ B ) – n ( A ∩ B) = n ( A ) + n ( B ) – n ( A ∩ B), which verifies ( ) (iii) If A, B and C are finite sets, then n ( A ∪ B ∪ C ) = n ( A ) + n ( B ) + n ( C ) – n ( A ∩ B ) – n ( B ∩ C) – n ( A ∩ C ) + n ( A ∩ B ∩ C ) ... ( ) In fact, we have n ( A ∪ B ∪ C ) = n (A) + n ( B ∪ C ) – n [ A ∩ ( B ∪ C ) ] [ by ( ) ] = n (A) + n ( B ) + n ( C ) – n ( B ∩ C ) – n [ A ∩ ( B ∪ C ) ] [ by ( ) ] Since A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C ), we get n [ A ∩ ( B ∪ C ) ] = n ( A ∩ B ) + n ( A ∩ C ) – n [ ( A ∩ B ) ∩ (A ∩ C)] = n ( A ∩ B ) + n ( A ∩ C ) – n (A ∩ B ∩ C) Therefore n ( A ∪ B ∪ C ) = n (A) + n ( B ) + n ( C ) – n ( A ∩ B ) – n ( B ∩ C) – n ( A ∩ C ) + n ( A ∩ B ∩ C ) This proves ( ). Example If X and Y are two sets such