Find the truth sets for M(x) ^ N(x) using N and Z
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Question
Find the truth sets for M(x) ^ N(x) using N and Z
![M(x): |x+4|<=10
N(x): |x+4|>7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F533810fa-4d07-45bb-8130-109ce090576c%2F8d3801cd-b98f-4f4f-a165-b8a2bc7db1bc%2F9qipc34_processed.png&w=3840&q=75)
Transcribed Image Text:M(x): |x+4|<=10
N(x): |x+4|>7
Expert Solution
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Step 1
Using the N universal set:
The N universal set consists of all positive integers from 1 to infinity.
To find the truth set for the conjunction M(x) ^ N(x) in the N universal set, we need to find the values of x that satisfy both inequalities:
M(x): |x+4| <= 10 N(x): |x+4| > 7
From M(x), we know that:
-10 <= x+4 <= 10
-14 <= x <= 6
From N(x), we know that:
x+4 > 7 or x+4 < -7
x > 3 or x < -11
The values of x that satisfy both M(x) and N(x) are -11, -10, -9, -8, -7, -6, -5, -4, -3, 4, 5, 6.
Therefore, the truth set for M(x) ^ N(x) in the N universal set is x ∈ {-11, -10, -9, -8, -7, -6, -5, -4, -3, 4, 5, 6}.
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