Answered: For this problem, the domain is the set…

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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Question

For this problem, the domain is the set of all solar system objects:
P(x) means x is a Planet
M(x) means x is a Moon
O(x, y) means x orbits y

Formulate the following statements using predicate logic.

1. All planets orbit the sun and all moons orbit a planet.
2. Some planets have no moon.
3. Some planets have two or more moons.
4. Some objects orbit the sun that are not planets
5. Everything that orbits the sun is a planet.
(Also prove that this statement is the negation of the previous statement)

Expert Solution

Step 1: Writing the given information

“Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts for you. To get the remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.”

The domain is the set of all solar system objects.

$P (x)$ means $x$ is a planet, $M (x)$ means $x$ is a moon, and $O (x, y)$ means $x$ orbits $y$ .

1. Statement: All planets orbit the sun and all moons orbit a planet.

We can break it into two parts. The first part is, for all $x$ , if $x$ is a planet, then $x$ orbits sun.

This can be written as $for all x open parentheses P open parentheses x close parentheses rightwards arrow O open parentheses x comma " text sun end text " close parentheses close parentheses$ .