0 votes 0 votes Mathematical Logic mathematical-logic + – vaishali jhalani asked Dec 16, 2016 vaishali jhalani 682 views answer comment Share Follow See all 16 Comments See all 16 16 Comments reply Show 13 previous comments Sushant Gokhale commented Dec 24, 2016 reply Follow Share P^S is SOP term, right? But there is existential quantifier. So, when p=1 and S=1, the entries would be 1 only sometimes. Now, Lets ignore P^S. So, remaining entries ( excluding the 2 premises)would be 1 or dont care, right? Now, lets look at the conclusion. $\exists$x { r(x) ^ s(x) } which corresponds to third column from left. So, you want 3rd column to be all 1's atleast once or for some instances. Lets go back to $\exists$x { P(x) ^ S(x) } So, now mark all 1's for this function because there exists atleast one instance where both P(x) and S(x) is true. Now, for this instance, just combine the 1's with dont care. So, 2nd statement is also valid. I think I gave wrong answer initially :) 0 votes 0 votes Akriti sood commented Dec 24, 2016 reply Follow Share yes..i got that..thankyou so much..:-) 1 votes 1 votes Shiva Sagar Rao commented May 7, 2021 reply Follow Share https://gateoverflow.in/107257/mock1-ace 0 votes 0 votes Please log in or register to add a comment.