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(A uu B)' is equal to...

`(A uu B)'` is equal to

A

`A' uu B'`

B

`A'nn B'`

C

`AnnB`

D

`A uuB`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the expression `(A ∪ B)'`, we will use De Morgan's Laws, which state that the complement of a union of two sets is equal to the intersection of their complements. ### Step-by-Step Solution: 1. **Identify the Expression**: We start with the expression `(A ∪ B)'`, which represents the complement of the union of sets A and B. 2. **Apply De Morgan's Law**: According to De Morgan's Laws, the complement of the union of two sets can be expressed as: \[ (A ∪ B)' = A' ∩ B' \] This means that the complement of the union of sets A and B is equal to the intersection of the complements of A and B. 3. **Conclusion**: Therefore, the expression `(A ∪ B)'` simplifies to: \[ A' ∩ B' \] ### Final Answer: The expression `(A ∪ B)'` is equal to \( A' ∩ B' \). ---
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