Consider the sentence (3xP(x) ^ 3xQ(x)) 3x(P(x) ^ Q(x)). Which of the following is true? A. The sentence is valid. OB. The sentence is not valid. It is false under the interpretation where x ranges over the positive integers, P(x) is x = 1 (mod 3)" and Q(x) is "x = 2 (mod 6)". "1 OC. The sentence is not valid. It is false under the interpretation where x ranges over the positive integers, P(x) is x = 1 (mod 3)" and Q(x) is "x = 4 (mod 6)". OD. The sentence is not valid. It is false under the interpretation where x ranges over the positive integers, P(x) is " 2x 1 (mod 3)" and Q(x) is "2x = 3 (mod 6)".
Consider the sentence (3xP(x) ^ 3xQ(x)) 3x(P(x) ^ Q(x)). Which of the following is true? A. The sentence is valid. OB. The sentence is not valid. It is false under the interpretation where x ranges over the positive integers, P(x) is x = 1 (mod 3)" and Q(x) is "x = 2 (mod 6)". "1 OC. The sentence is not valid. It is false under the interpretation where x ranges over the positive integers, P(x) is x = 1 (mod 3)" and Q(x) is "x = 4 (mod 6)". OD. The sentence is not valid. It is false under the interpretation where x ranges over the positive integers, P(x) is " 2x 1 (mod 3)" and Q(x) is "2x = 3 (mod 6)".
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
![Consider the sentence (ExP(x) ^ 3xQ(x)) → 3x(P(x) ^ Q(x)). Which of the following is true?
A. The sentence is valid.
OB. The sentence is not valid. It is false under the interpretation where x ranges over the positive integers, P(x) is
x = 1 (mod 3)" and Q(x) is "x = 2 (mod 6)".
OC. The sentence is not valid. It is false under the interpretation where x ranges over the positive integers, P(x) is "
x = 1 (mod 3)" and Q(x) is "x = 4 (mod 6)".
OD. The sentence is not valid. It is false under the interpretation where x ranges over the positive integers, P(x) is
2x = 1 (mod 3)" and Q(x) is "2x = 3 (mod 6)".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4535230f-c7e9-4901-b23a-065a860c8fbe%2F1bdc7f13-c3f8-4905-876d-76535fbca493%2Fru6tmxs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the sentence (ExP(x) ^ 3xQ(x)) → 3x(P(x) ^ Q(x)). Which of the following is true?
A. The sentence is valid.
OB. The sentence is not valid. It is false under the interpretation where x ranges over the positive integers, P(x) is
x = 1 (mod 3)" and Q(x) is "x = 2 (mod 6)".
OC. The sentence is not valid. It is false under the interpretation where x ranges over the positive integers, P(x) is "
x = 1 (mod 3)" and Q(x) is "x = 4 (mod 6)".
OD. The sentence is not valid. It is false under the interpretation where x ranges over the positive integers, P(x) is
2x = 1 (mod 3)" and Q(x) is "2x = 3 (mod 6)".
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