I'm trying to solve the following five problems where I'm asked to translate these English sentences into FOL by using Tarski's World symbols. I'll appreciate it very much if anyone can help me confirm my solutions to the problems.
c is to the right of a, provided it (i.e., c) is small.
c is to the right of d only if b is to the right of c and left of e.
- If e is a tetrahedron, then it's to the right of b if and only if it is also in front of b.
- e is in front of d unless it (i.e., e) is a large tetrahedron.
- d is the same shape as b only if they are the same size.
1) RightOf(c,a) ⇒ Small(c)
2) RightOf(c,d) ⇒ (RightOf(b,c) ∧ LeftOf(b,e))
3) Tet(e) ⇒ (RightOf(e,b) ⇔ FrontOf(e,b)): I'm not very certain for this problem. Can it be that: (Tet(e) ⇒ RightOf(e,b)) ⇔ (Tet(e) ⇒ LeftOf(e,b)) the correct solution? Because if the iff symbol is in between RightOf(e,b) and FrontOf(e,b), then it only shows the iff relation between these two and not related Tet(e) at all.
4) ¬(Large(e) ∧ Tet(e)) ⇒ FrontOf(e,d):
For this problem, the "Q unless P" translates to "If ¬P then Q", at first I thought of using ¬(Large(e) ∨ Tet(e)), but on the second thought that if we have "Small Tetrahedron" it will still satisfy the "If ¬P" aka if it's the case that P is large Tetrahedron. So I used conjunction instead.
5)SameShape(d,b) ⇒ SameSize(d,b)