Chapter 3.3, Problem 20ES

Recall that reversing that order of the quantifiers in a statement with two different quantifiers may Change the truth value of statement---but it does not necessarily do so. All the statements in the pairs below refer to the Tarski world of Figure 3.3.1. In each pair, the order of the quantifiers is reversed but everything else is the same. For each pair, the order of the quantifiers is reversed but everything else is the same. For each pair determine whether the statements have the same of opposite truth values. Justify your answers.
a. (1)For every square y there is a triangle x such that x and y have different colors.
(2) There is a triangle x such that for very squire y, x and y have different colors.

b. (1) For every circle y there is a square x such that x and y have the same color.

(2) There is a square x such that for every circle y, x and y have the same color.