0 votes 0 votes closed with the note: Doubt cleared Let T(x,y) mean that student x likes cuisine y, where the domain for x consists of all students at your school and the domain y consists of all cuisines. What is meant by the below expression? ∀x∀z∃y ((x≠z)→ ∼(T(x,y) ^ T(z,y))) Mathematical Logic mathematical-logic discrete-mathematics kenneth-rosen + – Ayush Upadhyaya asked Apr 18, 2017 closed Apr 19, 2017 by Ayush Upadhyaya Ayush Upadhyaya 498 views comment Share Follow See all 4 Comments See all 4 4 Comments reply Kapil commented Apr 18, 2017 reply Follow Share Two students cannot like same cuisine OR In other words, There exists atleast one cuisine which cannot be liked by two students. 0 votes 0 votes Ayush Upadhyaya commented Apr 18, 2017 reply Follow Share But the answer was given like this: "For every distinct pair of students at your school there is a cuisine that either or both of them may not like it" hows that possible? 0 votes 0 votes Prashant. commented Apr 19, 2017 reply Follow Share ∀x∀z∃y ((x≠z)→ ∼(T(x,y) ^ T(z,y))) ∀ means For all or Every , ∃ means There exist or Atleast one. So statement saying: For all x For all z There exist Atleast one y such that if z is not euqal to z ( x and y are different person) then not( x like y and z like y). For all x For all z There exist Atleast one y such that if z is not euqal to z ( x and y are different person) then (not x like y) or not (z like y). For all x For all z There exist Atleast one y such that if z is not euqal to z ( x and y are different person) then ( x not like y) or (z not like y). Means For every distinct pair of students at your school there is a cuisine that either one or both of them may not like it 1 votes 1 votes Ayush Upadhyaya commented Apr 19, 2017 reply Follow Share Okay, got it. Thanks prashant. 0 votes 0 votes Please log in or register to add a comment.