Answered: Let P(x) be the statement "x^2−x−20⩽0".…

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

Related questions

Question

Let P(x) be the statement "x^2−x−20⩽0".

a. If the domain consists of −4,0,1 and 2, then "∀x,P(x)" is: True or False?

b. If the domain consists of -5,-4,0, and 6, then "∀x,P(x)" is: True or False?

Now let Q(x) be the statment "x^2 - x - 20 > 0."

a. If the domain consists of -5,2,4, and 6, then "∃x such that Q(x)" is:True or False?

b. If the domain consists of -1,0,1, and 4, then "∃x such that Q(x)" is: True or False?

Expert Solution

Step 1

Given:

Here is the given statements,

1. $P (x) = x^{2} - x - 20 \leq 0$

To find:

Is it true or false that $" \forall x, P (x) "$ is true if the domain contains the values $- 4, 0, 1,$ and $2$ .
Is the statement $" \forall x, P (x) "$ True or False if the domain contains the values $- 5, - 4, 0,$ and $6$ ?

2. $Q (x) = x^{2} - x - 20 > 0$

To find:

If the numbers $- 5, 2, 4,$ and $6$ make up the domain, is the statement " $\exists x$ such that $Q (x)$ " true or false?
Is it true or false if the domain consists of $- 1, 0, 1,$ and $4$ if " $\exists x$ such that $Q (x)$ "?