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Find the truth sets for M(x) ^ N(x) using N and Z

Find the truth sets for M(x) ^ N(x) using N and Z

Database System Concepts
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
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Find the truth sets for M(x) ^ N(x) using N and Z

M(x): |x+4|<=10 N(x): |x+4|>7
Transcribed Image Text:M(x): |x+4|<=10 N(x): |x+4|>7
Expert Solution
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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