27 votes 27 votes Let $*$ be defined as $x * y = \bar{x} + y$. Let $z = x * y$. Value of $z * x$ is $\bar{x} + y$ $x$ $0$ $1$ Digital Logic gate1997 digital-logic normal boolean-algebra + – Kathleen asked Sep 29, 2014 • edited Feb 10, 2018 by go_editor Kathleen 5.5k views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments Ashwani Kumar 2 commented Nov 29, 2017 reply Follow Share opton a) $z*x=z+x=(x*y)+x=x+y+x=x+y$ 1 votes 1 votes Ashwin Kulkarni commented Nov 29, 2017 reply Follow Share z + x= x+y+x = x+y 0 votes 0 votes Deepak Poonia commented Oct 15, 2021 i edited by Deepak Poonia Jul 16, 2022 reply Follow Share $\color{red}{\text{Find Detailed Video Solution Below:}}$https://youtu.be/AG6rGfFzAdw 5 votes 5 votes Please log in or register to add a comment.
Best answer 38 votes 38 votes Answer is option B. $z* x = {(x*y)} * x$ $=\left(\bar{x} + y\right) * x$ $=\overline{\bar{x} + y} + x $ $x.\bar{y} + x = x$ Arjun answered Dec 21, 2014 • edited Jun 22, 2018 by Milicevic3306 Arjun comment Share Follow See all 7 Comments See all 7 7 Comments reply Show 4 previous comments Shiva Pandey commented Jan 21, 2015 reply Follow Share my pleasure sir 1 votes 1 votes coder_yash commented Dec 29, 2020 reply Follow Share @Arjun Sir, since nature of * is not given but if we assume nature of * is right-associative then, $z*x = x * y *x.$ $ z = x * (y * x)$ $ z = x * (\bar{ y} + x)$ $z = \bar{x} + \bar{y} + x$ $z = 1 + \bar{y} = 1.$ Please tell me where am I doing mistake? 0 votes 0 votes Deepak Poonia commented Oct 13, 2021 reply Follow Share Sir, since nature of * is not given but if we assume nature of * is right-associative then,……… Please tell me where am I doing mistake? The given operation $*$ is Not associative, So that’s the mistake. Note that $*$ is Implication operation, i.e. $x*y = x \rightarrow y$, and Implication operation is NOT associative. Now, we can write $z*x = (z)*x = (x*y)*x.$ Also note that Implication operation is NOT Commutative. 3 votes 3 votes Please log in or register to add a comment.
8 votes 8 votes The answer is Option (b). Given $x*y = x' +y$ $z= x*y$ Therefore $z = x'+y$ $z*x = z' +x$ $= (x'+y)' +x$ $= x.y' + x$ $= x(y' +1)$ $= x$ Answer $z*x = x$ Prateek K answered Nov 29, 2017 • edited Oct 26, 2018 by kenzou Prateek K comment Share Follow See all 2 Comments See all 2 2 Comments reply Ashwin Kulkarni commented Nov 29, 2017 reply Follow Share He asked something different. He didn't put that compliment in this question . 0 votes 0 votes Prateek K commented Nov 29, 2017 reply Follow Share Question Edited, now the question is correct. 0 votes 0 votes Please log in or register to add a comment.
7 votes 7 votes Z*X=(X*Y)*X =(Xc+Y)c+X =X.Yc+X =X(1+Yc) =X Aboveallplayer answered Jan 3, 2017 Aboveallplayer comment Share Follow See 1 comment See all 1 1 comment reply Vinit Dhull 1 commented Sep 16, 2017 reply Follow Share Which rule is applied to change from step 1 to 2 ? 0 votes 0 votes Please log in or register to add a comment.
3 votes 3 votes Answer : Option B HeadShot answered Sep 15, 2018 HeadShot comment Share Follow See all 0 reply Please log in or register to add a comment.