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Kenneth Rosen Edition 7 Exercise 1.5 Question 25 (Page No. 66)

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Translate each of these nested quantifications into an English statement that expresses a mathematical fact. The domain in each case consists of all real numbers.

  1. $\exists x \forall y (xy=y)$
  2. $\forall x\forall y (((x<0) \wedge (y<0)) \rightarrow (xy>0))$
  3. $\exists x \exists y ((x^2 >y) \wedge (x<y))$
  4. $\forall x \forall y \exists z (x+y =z)$
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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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