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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?

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?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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. Px=x2−x−20≤0

To find:

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

2. Qx=x2−x−20>0

To find:

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