ISRO2014-56

Question

Which of the following is not valid Boolean algebra rule?

• A. $\text{X.X = X}$
• B. $\text{(X+Y).X = X}$
• C. $\overline{X}+\text{XY = Y}$
• D. $\text{(X+Y).(X+Z) = X + YZ}$

Comments

C.

Answer 1

Answer is C

x' + xy = (x' + x)(x' + y) = x' + y

Answer 2

ans is C x'+xy =(x'+x)(x'+y)=1.(x'+y)=x'+y which is not equal to y

a)is true as X.X=X    b)(X+Y).X=XX+XY=X+XY=X(1+Y)=X IS ALSO TRUE

D)is true as xx+xz+yx+yz=x+xz+yx+yz=x(1+z+y)+yz=x+yz

Answer 3

$X.X = X $OPTION(A) TRUE

$(X+Y)X = X+XY=X(1+Y)=X $OPTION (B) TRUE

$(X’+XY) = (X’+X)(X’+Y) = X’+Y ≠ Y$ OPTION (C) FALSE

$(X+Y)(X+Z) = XX+XZ+XY+YZ=X+XZ+XY+YZ=X(1+Z+Y) + YZ = X+YZ$ OPTION (D) TRUE

so only false rule is c

answer (c)

Answer 4

A.X.X=X is valid

B.(X+Y)X=X is valid using truth table.

C.X'+XY=Y is not valid using truth table

D.(X+Y)(X+Z)=X+YZ is valid by absorption rule