Question

What is the first order predecate calculus statement equivalent to the following ? Every teacher is likes by some student

• A. $\forall \left(x\right)[teacher\left(x\right)\to \exists \left(y\right)[student\left(y\right)\to likes(y,x)]]$
• B. $\forall \left(x\right)[teacher\left(x\right)\to \exists \left(y\right)[student\left(y\right)\wedge likes(y,x)]]$
• C. $\exists \left(y\right)\forall \left(x\right)[teacher\left(x\right)\to \exists \left(y\right)[student\left(y\right)\wedge likes(y,x)]]$
• D. $\forall \left(x\right)[teacher\left(x\right)\wedge \exists \left(y\right)[student\left(y\right)\to likes(y,x)]]$

Answer 1

The correct option is B $\forall \left(x\right)[teacher\left(x\right)\to \exists \left(y\right)[student\left(y\right)\wedge likes(y,x)]]$

Every teacher is liked by some student : then the logical expression is$\forall \left(x\right)[teacher\left(x\right)\to \exists \left(y\right)[student\left(y\right)\wedge likes(y,x)]]$
Where likes (y, x) means y likes x, such that y represent the student and x represents the teacher.