Which of the following is not a valid expression of Boolean algebra?

2022

Which of the following is not a valid expression of Boolean algebra?

  1. A.

    ~x + (y * ~z) + x + ~y = 1

  2. B.

    x * ~y + ~x * y + ~x * ~y = 1

  3. C.

    ~(x + y + z) = ~x * ~y * ~z

  4. D.

    x * ~y + ~x * y + x * y = x + y

Attempted by 119 students.

Show answer & explanation

Correct answer: B

A)
~x + (y·~z) + x + ~y = 1
Since ~x + x = 1, the whole expression becomes 1. ✅ Valid

B)
x·~y + ~x·y + ~x·~y = 1
Factor:
~x·y + ~x·~y = ~x(y + ~y) = ~x
So expression becomes:
x·~y + ~x
This is not always 1. ❌ Not valid

C)
~(x + y + z) = ~x·~y·~z
This is De Morgan’s law. ✅ Valid

D)
x·~y + ~x·y + x·y = x + y
LHS simplifies to x + y. ✅ Valid

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