Which of the following is the complement of the boolean function.

A'B + CD' + A'B + CD'

The correct answer is Option 3) (A + B')(C' + D).

Key Points

Given Boolean function: A'B + CD' + A'B + CD'

• First simplify the given expression:
  • A'B + A'B = A'B (redundant term)
  • CD' + CD' = CD' (redundant term)
• So, the simplified function = A'B + CD'

Now, we are asked to find the complement of this function:

Let F = A'B + CD'

Then the complement is: F' = (A'B + CD')'

Apply De Morgan’s Law:

• (A'B + CD')' = (A'B)' · (CD')'
• (A'B)' = A + B'
• (CD')' = C' + D

Therefore, F' = (A + B')(C' + D)

Hence, the correct answer is: Option 3) (A + B')(C' + D)