34 votes 34 votes The truth table ${\begin{array}{|c|c|c|}\hline \textbf{X}& \textbf{Y}& \textbf{(X,Y)} \\\hline 0& 0& 0 \\ \hline 0& 1&0\\ \hline 1& 0& 1 \\\hline 1& 1& 1 \\\hline \end{array}}$ represents the Boolean function $X$ $X + Y$ $X \oplus Y$ $Y$ Digital Logic gatecse-2012 digital-logic easy boolean-algebra + – gatecse asked Aug 5, 2014 edited Apr 15, 2019 by ajaysoni1924 gatecse 4.3k views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply Abhrajyoti00 commented Jan 1, 2023 reply Follow Share This should be tagged as super-easy / trivial/ take the marks for free question. The X column is as it is given in f(X,Y) 0 votes 0 votes gatecse commented Jan 1, 2023 reply Follow Share @Abhrajyoti00 Still I don’t think not even 50% of GATE takers would have got this correct. 0 votes 0 votes Abhrajyoti00 commented Jan 1, 2023 reply Follow Share @gatecse Sir, Why? Because of the % of qualifying students? 0 votes 0 votes gatecse commented Jan 1, 2023 reply Follow Share yes, and I have been seeing the answers entered by students in the Pragy’s app :) In fact less than 1% of the GATE aspirants are solving the questions – rest are studying the given solutions – so easy/normal etc are only applicable to the 1%. 2 votes 2 votes Please log in or register to add a comment.
Best answer 46 votes 46 votes Whenever $X$ is true $(X,Y)$ is true and whenever $X$ is false $(X,Y)$ is false, so the answer is (A) $X$. Omesh Pandita answered Aug 5, 2014 selected May 19, 2019 by akash.dinkar12 Omesh Pandita comment Share Follow See all 0 reply Please log in or register to add a comment.
7 votes 7 votes f(x,y)= xy' + xy = x(y'+y) = x Punit Sharma answered Nov 3, 2018 Punit Sharma comment Share Follow See all 0 reply Please log in or register to add a comment.
5 votes 5 votes Using $k-$map method,we get $f(x,y) = x.$ Lakshman Bhaiya answered Oct 3, 2019 Lakshman Bhaiya comment Share Follow See all 2 Comments See all 2 2 Comments reply Abhrajyoti00 commented Jan 1, 2023 reply Follow Share Why do we even need a K-Map for this q? The X column is as it is given in f(X,Y) 2 votes 2 votes mahendrapatel commented Jan 26, 2023 reply Follow Share Multiple approaches 0 votes 0 votes Please log in or register to add a comment.