What is the first order predicate calculus statement equivalent to the following?
"Every teacher is liked by some student"
Answer is B. In simpler way we can say If X is a teacher then there exists some Y who is a student and likes X.
A choice: If X is a teacher, then there exists a Y such that if Y is a student, then Y likes X.
C choice: There exist a student who likes all teachers.
D choice: Everyone is a teacher and there exists a Y such that if Y is student then y likes X. Assuming one cannot be both student and teacher at same time, this just means, everyone is a teacher.
"Every teacher is liked by some student" is equivalent to If (for all people ) person is the teacher then liked by some student.
Option B say exactly that. But Option D says (for all people ) person is the teacher and liked by some student.
Student likes which is and relation eliminates option (a) and (d) there is some students therefore ∃(y) it eliminates option c so option b is answer
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