Which of the following is correct? |
$n (A ∪ B) = n (A) + n (B) + n (A ∩ B)$ $n (A ∪ B) = n (A) – n (B) – n (A ∩ B)$ $n (A ∪ B) = n (A) + n (B) – n (A ∩ B)$ $n (A ∩ B) = n (A) + n (B) + n (A ∪ B)$ |
$n (A ∪ B) = n (A) + n (B) – n (A ∩ B)$ |
The correct answer is Option (3) → $n (A ∪ B) = n (A) + n (B) – n (A ∩ B)$ In the Venn diagram, $n (A ∪ B) = a + b + c$ $n(A) = a + c, n(B) = b + c$ and $n (A ∩ B) = c$ $n (A) + n (B) – n (A ∩ B) = (a + c) + (b + c)-c = a + b + c$ Hence, $n (A ∪ B) = n (A) + n (B) – n (A ∩ B)$. |