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

Chapter 3, Problem 20

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Recall that reversing the order of the quantifiers in a statement with two different quantifiers may change the truth value of the statementbut it does not necessarily do so. All the statements in the pairs on the next page 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, determine whether the statements have the same or opposite truth values. Justify your answers.

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