28 votes 28 votes A Boolean function $x’y’ + xy + x’y$ is equivalent to $x' + y'$ $x + y$ $x + y'$ $x' + y$ Digital Logic gatecse-2004 digital-logic easy boolean-algebra + – Kathleen asked Sep 18, 2014 Kathleen 7.7k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Vaibhav Chauhan commented Jul 29, 2020 reply Follow Share One simple way of doing such type of questions is : step1 - Draw the k-map for the given inputs step2 - group the minterms and the resultant is your answer. 2 votes 2 votes mohit7891 commented Nov 6, 2023 reply Follow Share you can think in minterm,maxterm way also. 0 votes 0 votes Please log in or register to add a comment.
Best answer 33 votes 33 votes Answer is option D. $x'y' + x'y = x'(y+y') = x'$ $x' + xy = x' + y$ Arjun answered Oct 20, 2014 edited Jun 29, 2018 by Milicevic3306 Arjun comment Share Follow See all 3 Comments See all 3 3 Comments reply flash12 commented Jan 5, 2018 reply Follow Share how x' + xy = x' + y ???? 0 votes 0 votes talha hashim commented Nov 2, 2018 reply Follow Share x' + xy = x'(y+y') + xy =x'y + x'y' + xy =x'y + x'y + x'y' + xy (because AB+AB+AB+.......................=AB) =(x'y + x'y') + (x'y + xy) =x'(y+y') + y(x+x') =x'+y 4 votes 4 votes Lakshman Bhaiya commented Nov 2, 2018 reply Follow Share @lash12 how x' + xy = x' + y ???? $x' + x.y$ [ In this case $+$ is distributed over $.$ (In boolean algebra this is also possible.] $x' + x.y=(x'+x).(x'+y)$ $x' + x.y=(1).(x'+y)$ $ [\bar{A}+A=1]$ $x' + x.y=(x'+y)= x'+y$ 8 votes 8 votes Please log in or register to add a comment.
13 votes 13 votes answer - D use K map ankitrokdeonsns answered Oct 19, 2014 ankitrokdeonsns comment Share Follow See 1 comment See all 1 1 comment reply Puja Mishra commented Dec 18, 2017 reply Follow Share Use distribution rule ... 1 votes 1 votes Please log in or register to add a comment.
5 votes 5 votes = X'Y' + XY +X'Y = X' ( Y + Y' ) + Y ( X + X') = X' + Y hence option d is correct air1ankit answered Dec 29, 2017 air1ankit comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes Using K map for two variables y' y x' 1 1 x 0 1 Tables for expression given looks like this from this we get: x'+y Shubham Mahidhar answered Oct 28, 2018 Shubham Mahidhar comment Share Follow See 1 comment See all 1 1 comment reply AksharaMakwana commented Jan 12 reply Follow Share x’y’ + xy + x’y x’(y’+y) + xy [y’+y = 1] x’ + xy [distribution law] (x’+x) (x’+ y) [x’+x = 1] x’+y 0 votes 0 votes Please log in or register to add a comment.