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Question : 6 of 33

Marks: +1, -0

If n(∪) = 750, n(A) = 250, n(B) = 350, n(A ∩B), is = 150, then n(A′ ∩ B′) is:

200
250
300
350
None of the above

Solution: 👈: Video Solution

Concept:

By De Morgan's law,

A' \cap B' = (A \cup B)'

.

Explanation:

Given

n(U)=750

,

n(A)=250

,

n(B)=350

, and

n(A \cap B)=150

.

First find

n(A \cup B)

using

n(A \cup B)=n(A)+n(B)-n(A \cap B)

.

So,

n(A \cup B)=250+350-150=450

.

Then,

n(A' \cap B')=n((A \cup B)')=n(U)-n(A \cup B)

.

Thus,

n(A' \cap B')=750-450=300

.

Answer:

n(A' \cap B')=300

, so the correct option is C.

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