interpreting mixed quantifier I want to interpret the below sentences...


*

*∀x∃y(Cube(x) → (Tet(y) ∧ LeftOf(x, y)))

*∃y∀x (Cube(x) → (Tet(y) ∧ LeftOf(x, y)))


Actually I could interpret the first sentence.
Meaning: Every Cube is left of some Tet
But.. I can't interpret the second sentence.
Let (Cube(x) → (Tet(y) ∧ LeftOf(x, y))) be P(x, y).
There exits some y such that for all x P(x, y) is ture?
.. I don't know.......
please help me to know about it!!
 A: Take it one step at a time. You have $$\exists y\forall x\left(\operatorname{Cube}(x)\to\Big(\operatorname{Tet}(y)\land\operatorname{LeftOf}(x,y)\Big)\right)\;.\tag{1}$$ The first step in translating it is straightforward: just expand the quantifiers and predicates into words.

(a) There is a $y$ such that for every $x$, if $x$ is a cube, then $y$ is a tetrahedron and $x$ is to the left of $y$.

Now notice that if there is at least one cube, the statement y is a tetrahedron does not depend in any way on $x$. We could just as well say:

(b) There is a $y$ such that $y$ is a tetrahedron, and for every $x$, if $x$ is a cube, then $x$ is to the left of $y$.

It would mean the same thing. 
The qualifier if there is at least one cube is necessary, because if there are no cubes, $(1)$ and (a) are vacuously true. To keep matters simple, I’ll assume for the moment that there is at least one cube and derive a simple English equivalent; once we have that, we can modify it to get rid of the extra assumption.
Now we can start turning (b) into more ordinary English:

(c) There is a tetrahedron such that every cube is to the left of that tetrahedron.

Or in even more straightforward English:

(d) There is a tetrahedron that is to the right of every cube.

Remember, though, this was equivalent to $(1)$ and (a) only on the extra assumption that there is at least one cube, and that $(1)$ and (a) are vacuously true if there are no cubes. To make (d) equivalent to $(a)$, we must add an alternative:

(e) Either there are no cubes, or there is a tetrahedron that is to the right of every cube.

A: The exact paraphrase of the second sentence would be: there exists y such that for all x if x is a cube than y has property tet and it holds that leftof(x,y). Also your abbreviation seems correct.
