Question

Which of the following is not a valid expression of Boolean Algebra?
1. x + x.y = x
2. x'.y + x.y = y
3. x'.y' + x.y = x
4. (x + y + z)' = x'.y'.z'

Answer 1

Correct Answer - Option 3 : x'.y' + x.y = x

Option 1 : x + x.y = x 

LHS = x + x.y = x(1 + y) = x.1 = x   // Boolen Expression law

Option 2 : x'.y+x.y=y

LHS =x'.y+x.y = y(x'+x)=y(1)=y // Boolen Expression law

Option 3 :x'.y'+x.y=x

XNOR(x, y) = x ⊙ y = x.y + x'.y' // Exclusive NOR Rule

Option 4 : (x + y + z)' = x'.y'.z'

(x + y + z)' = x'.y'.z' // Folloe Demorgan's Law

So the correct Answer is Option 3