Math 199 (Assignments)

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1. Consider the proposition: $(\forall x\in\R)(\exists y\in\R)(xy=1)$.
   1. What is the negation of this statement?
   2. Translate both statements into words.
   3. One of the statements must be true; which is it? Prove it.
2. Consider the proposition: $(\exists x\in\R)(\forall y\in\R)(xy=y)$.
   1. What is the negation of this statement?
   2. Translate both statements into words.
   3. One of the statements must be true; which is it? Prove it.
3. Consider the proposition: $(\forall x\in\R)(\exists y\in\R)(x=y^2)$.
   1. What is the negation of this statement?
   2. Translate both statements into words.
   3. One of the statements must be true; which is it? Prove it.

Math 199 (Fall 2019) web pages Created: 2 Oct 2019 Last modified: 2 Oct 2019 at 6:49 PM Comments to: dpvc@union.edu

Assignments