Recall that reversing the order of the quantifiers in a statement with two different quant...

Recall that reversing the order of the quantifiers in a statement with two different quantifiers may change the truth value of the statement—but it does not necessarily do so. All the statements in the pairs below refer to the Tarski world of Figure. In 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 or opposite truth values. Justify your answers.

a. (1) For all squares y there is a triangle x such that x and y have different color.

(2) There is a triangle x such that for all squares y, x and y have different colors.

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

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