Discrete Homework Questions 4. Consider the statement Vx e R*, x > .(a) Show that the statement is false.(b) Use quantifiers to write its negation.

Name: Discrete Homework Questions 4. Consider the statement Vx e R*, x > .(a
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Discrete Homework Questions 4. Consider the statement Vx e R*, x > .(a) Show that the statement is false.(b) Use quantifiers to write its negation.

Let, the given statement is denoted by p i.e. p:∀x∈ℝ+, x>1x Since ℝ+ contains the interval 0,1,…

Answered: 4. Consider the statement Vx e R*, x >…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

Discrete Homework Questions

4. Consider the statement Vx e R*, x > .
(a) Show that the statement is false.
(b) Use quantifiers to write its negation.

Expert Solution

Step 1

Let, the given statement is denoted by $p$ i.e.

$p : \forall x \in ℝ^{+}, x > \frac{1}{x}$

Since $ℝ^{+}$ contains the interval $(0, 1)$ , let us consider an arbitrary $x \in (0, 1)$

Now,

$\begin{array}{rcl} 0 & < & x < 1 \\ 1 & < & \frac{1}{x} \end{array}$

Since, $x < 1$ , therefore $\frac{1}{x} > 1$ implies $x < \frac{1}{x}$ . Thus, p is not true for all $x \in ℝ^{+}$ .

Hence, given statement p is false.

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Propositional Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions