8 votes 8 votes Which of the following is not valid Boolean algebra rule? $\text{X.X = X}$ $\text{(X+Y).X = X}$ $\overline{X}+\text{XY = Y}$ $\text{(X+Y).(X+Z) = X + YZ}$ Digital Logic digital-logic boolean-algebra isro2014 + – Isha Gupta asked Jun 23, 2016 edited Dec 7, 2022 by Lakshman Bhaiya Isha Gupta 4.1k views answer comment Share Follow See 1 comment See all 1 1 comment reply vijaycs commented Jun 23, 2016 reply Follow Share C. 0 votes 0 votes Please log in or register to add a comment.
Best answer 10 votes 10 votes Answer is C x' + xy = (x' + x)(x' + y) = x' + y Kapil answered Jun 23, 2016 selected Aug 26, 2016 by Prashant. Kapil comment Share Follow See all 0 reply Please log in or register to add a comment.
4 votes 4 votes 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 Sanjay Sharma answered Jun 23, 2016 edited Dec 5, 2017 by Meenakshi Sharma Sanjay Sharma comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes $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) Musa answered Aug 25, 2020 Musa comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes 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 Pranabesh Ghosh 1 answered Jun 23, 2016 Pranabesh Ghosh 1 comment Share Follow See all 0 reply Please log in or register to add a comment.