Practicing Success

Target Exam

CUET

Subject

Mathematics

Chapter

Sets

Question:

Which of the following is correct?

Options:

$n (A ∪ B) = n (A) + n (B) + n (A ∩ B)$

$n (A ∪ B) = n (A) – n (B) – n (A ∩ B)$

$n (A ∪ B) = n (A) + n (B) – n (A ∩ B)$

$n (A ∩ B) = n (A) + n (B) + n (A ∪ B)$

Correct Answer:

$n (A ∪ B) = n (A) + n (B) – n (A ∩ B)$

Explanation:

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, $n (A ∪ B) = n (A) + n (B) – n (A ∩ B)$.