Chapter 3.4, Problem 30ES

In exercises 28-32, reorder the premises in each of the arguments to show that the conclusion follows as a valid consequence from the premises. It may be helpful to rewrite the statements in if—then form and replace some of them by their centrapositives. Exercises 28-30 refer to the kinds of Tarski worlds discussed in Examples 3.1.13 and 3.3.1. Exercises 31 and 32 are adapted from Symbolic Logic by Lewis Carroll.*
1. If an object is above all the triangles, then it is above all the blue objects.
2. If an object is not above all the gray objects, then it is not a square.
Every black object is a square.

4. Every object that is above all the gray objects is above all the triangles.
$\therefore$ If an object is black, then it is above all the blue objects.