Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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![25) Determine the truth value of the following statement if the domain of each variable consists of all
integers ?
3x: x³ = -1
[T/F]
26) Determine the truth value of the following statement if the domain of each variable consists of all
integers ?
3x: x² = 0
[T/F]
27) Determine the truth value of the following statement if the domain of each variable consists of all
integers ?
Vx: x²+2 <1
[T/F]
28) Determine the truth value of the following statement if the domain of each variable consists of all
integers?
Vx: x²
[T/F]
29) P (x) is the statement "x² < 8" and the domain consists of the positive integers less than 6. Write out the
proposition ExP(x) using disjunctions, conjunctions, and negations (i.e. rewrite the propositions
without using quantifiers).
a) (P(1) V P(2) VP(3) ✓ P(4) VP(5))
b)
c)
d)
(P(1) V P(2) VP(3) V P(4) VP(5) VP(6))
(P(1) ^ P(2) ^ P(3) ^ P(4) ^ P(5) ^ P(6))
(P(1) V P(2) V P(3) V P(4) V P(5) ✓ P(6) P(7))](https://content.bartleby.com/qna-images/question/1d6d343b-a62a-40ae-a805-92d7f4bddb64/df6e6c63-1166-45d5-8bf2-ce3162fa7f2f/hwosum_processed.jpeg)
Transcribed Image Text:25) Determine the truth value of the following statement if the domain of each variable consists of all
integers ?
3x: x³ = -1
[T/F]
26) Determine the truth value of the following statement if the domain of each variable consists of all
integers ?
3x: x² = 0
[T/F]
27) Determine the truth value of the following statement if the domain of each variable consists of all
integers ?
Vx: x²+2 <1
[T/F]
28) Determine the truth value of the following statement if the domain of each variable consists of all
integers?
Vx: x²
[T/F]
29) P (x) is the statement "x² < 8" and the domain consists of the positive integers less than 6. Write out the
proposition ExP(x) using disjunctions, conjunctions, and negations (i.e. rewrite the propositions
without using quantifiers).
a) (P(1) V P(2) VP(3) ✓ P(4) VP(5))
b)
c)
d)
(P(1) V P(2) VP(3) V P(4) VP(5) VP(6))
(P(1) ^ P(2) ^ P(3) ^ P(4) ^ P(5) ^ P(6))
(P(1) V P(2) V P(3) V P(4) V P(5) ✓ P(6) P(7))
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