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Kenneth Rosen Edition 7 Exercise 1.5 Question 20 (Page No. 66)

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Express each of these statements using predicates, quantifiers, logical connectives, and mathematical operators where the domain consists of all integers.

  1. The product of two negative integers is positive.
  2. The average of two positive integers is positive.
  3. The difference of two negative integers is not necessarily negative.
  4. The absolute value of the sum of two integers does not exceed the sum of the absolute values of these integers.
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Kenneth Rosen Edition 7 Exercise 1.5 Question 34 (Page No. 66)
Find a common domain for the variables $x,y$, and $z$ for which the statement $\forall x \forall y ((x \neq y) \rightarrow \forall z (z=x) \vee (z=y))$ is true and another domain for which it is false.
Find a common domain for the variables $x,y$, and $z$ for which the statement $\forall x \forall y ((x \neq y) \rightarrow \forall z (z=x) \vee (z=y))$ is true and anothe...
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