Try the fastest way to create flashcards
Question

# Is this statement true or false? Explain your answer. $\forall$ real numbers $x \exists$ an integer $n$ such that $n x$ is an integer.

Solution

Verified
Step 1
1 of 2

$\displaystyle \begin{array}{ c c } \boxed{\mathrm{False.}} & \mathrm{Suppose} \ x\ =\ \pi \ \mathrm{and} \ n\ =\ 3.\ \mathrm{Then} \ nx\ =\ 3\pi \ =\mathrm{which\ is\ not\ an\ integer.} \ \end{array}$

## Recommended textbook solutions #### Discrete Mathematics and Its Applications

7th EditionISBN: 9780073383095 (1 more)Kenneth Rosen
4,283 solutions #### Precalculus and Discrete Mathematics

3rd EditionISBN: 9780076214211Anthony L. Peressini, Mary Helen Wiltjer, Molly A. Rockstroh, Peter D. DeCraene, Steven S. Viktora, Ward E. Canfield, Zalman Usiskin
3,203 solutions #### Discrete Mathematics and Its Applications

8th EditionISBN: 9781259676512Kenneth Rosen
4,397 solutions #### Discrete Mathematics with Applications

5th EditionISBN: 9781337694193 (4 more)Susanna S. Epp
2,641 solutions