Maths · Union, intersection and complement of sets and their algebraic properties
Let =700, n(A)=400, n(B)=300, n(A \cap \) =300 . \) Then = \)
Let \( n(\cup)=700, n(A)=400, n(B)=300, n(A \cap \) \( \mathrm{B})=300 . \) Then \( \left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)= \)
- A. 300
- B. 400
- C. \) 350
- D. 250
Step-by-step solution
Using De Morgan's law, A' ∩ B' = (A ∪ B)'. First find n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 400 + 300 - 300 = 400. Then n((A ∪ B)') = n(U) - n(A ∪ B) = 700 - 400 = 300.
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