7. Эп Эт (п +m%3D4лп-т %3D1) 8. Эn Эт (п +m%3D4лп-т 32) 9. Уn Vm Эp (р %3D (т + п)2)
7. Эп Эт (п +m%3D4лп-т %3D1) 8. Эn Эт (п +m%3D4лп-т 32) 9. Уn Vm Эp (р %3D (т + п)2)
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
Related questions
Question
please answer 7 8 9 sub parts only
Transcribed Image Text:Problem 4: Determine the truth value of each of the following statements. We assume that the
domain for all variables consists of all integers.
1. Vn 3m (n? <m)
2. Эn Vm (n <m?)
3. Уn Эт (п+m3D0)
4. Эn Vm (пт %3D т)
5. 3n 3m (n² + m² =
6. Эn Эт (п?+ m? %3D 6)
7. Эп Эт (п + m%3D4лп- т 31)
8. Эn Эт (п +m%34 лп- т -2)
9. Уn Vm Эp (p %3 (т+n)2)
Expert Solution
Step 1
Symbols to know :
Existential quantification ∃x P(x) :
There exists an element x in the domain such that P(x).
Universal quantification ∀ x P(x) :
P(x) for all values of x in the domain.
7.∃n ∃m (n+m=4 ∧ n-m=1)
The above statement defines, "There exists two integers whose sum is 4 and whose difference is 1"
This statement is false, because the only answer for these two equations (n+m=4 and n-m=1) are n=5/2 and m=3/2 , these are not integers.
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