Mathematical Logic

Question

$Student(a)$ : $a$ is a student

$Loves(a,b)$ : $a$ loves $b$

Consider the following First Order Logic Statement:

$\exists x (Student(x)\ \Lambda\ \forall y(student(y)\ \Lambda\ \sim(x=y)\Rightarrow Loves(y,x)\ ))$

Which of the following is true:

• A. Every student loves some student
• B. Every student loves some other student
• C. There is a student who is loved by every other student
• D. There is a student who is not loved by every other student

I think here B) and C) both could be answer, Isnot it??

Comments

C sounds more appropriate. What is the answer?

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I think only C is correct !!

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yes C) ans

Answer 1

The statement says, there exists a student X, such that every other student Y loves that student. This clearly means that there is a student loved by every other student. Therefore, only c should be the answer.