2 votes 2 votes Difference bw a) and d) .... Shouldn't both be true for all real numbers? Mathematical Logic propositional-logic + – Pawan Kumar 2 asked Dec 31, 2017 Pawan Kumar 2 351 views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply joshi_nitish commented Dec 31, 2017 reply Follow Share @Pawan only D) is correct. in A) the equation is satisfied only for $x=-1$ and $x=0$ and for no other x except {-1,0} there does not exist any value of 'y' which satisfy above realtion. 2 votes 2 votes Anu007 commented Dec 31, 2017 reply Follow Share yes d should be correct D is saying there exist atleast one element i.e. x = x2 i.e. take 0 and (for all y) y = y 1 votes 1 votes Manu Thakur commented Dec 31, 2017 reply Follow Share A. For every x, there exists some y such that y-x = y+x^2. (not true) B. There exists some y such that y-x = y+ x^2 is true for every x. (not true) C. There exists some x such that x-y = x+y^2 is true for every y. (not true) D. For all y, there exists some x such that y-x = y+x^2. (true for x=0) 1 votes 1 votes joshi_nitish commented Dec 31, 2017 reply Follow Share @Manu D) is also true for $x=-1$ 2 votes 2 votes Pawan Kumar 2 commented Dec 31, 2017 reply Follow Share So a) is saying that there should exist some y such that for all x , x= - x2 should be satisfied eg x= { ........ -2,-1,0, 1 ,2 3.......} x= - x2 should be satisfied but its only possible for {0,-1} d) is saying that there should exist some x such that for all y , y= y should be satisfied which is true for x= 0 and -1.. Am i right joshi_nitish, Anu007 ,Manu Thakur sir ? 0 votes 0 votes Manu Thakur commented Dec 31, 2017 reply Follow Share as Nitish said, (D) is true for -1 also. 1 votes 1 votes Please log in or register to add a comment.