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Consider the sentences Vx3yP(x, y) and 3yVxP(x, y). Are these sentences true or false under the interpretation where x and y range over the positive integers and P(x, y) is "x divides y"? Vxy(x, y) is true, 3xP(x, y) is true ⒸVxy(x, y) is true, 3yVxP(x, y) is false Vx³yP(x, y) is false, 3yVxP(x, y) is true Vx³yP(x, y) is false, yvxP(x, y) is false

Consider the sentences Vx3yP(x, y) and 3yVxP(x, y). Are these sentences true or false under the interpretation where x and y range over the positive integers and P(x, y) is "x divides y"? Vxy(x, y) is true, 3xP(x, y) is true ⒸVxy(x, y) is true, 3yVxP(x, y) is false Vx³yP(x, y) is false, 3yVxP(x, y) is true Vx³yP(x, y) is false, yvxP(x, y) is false

Advanced Engineering Mathematics
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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Consider the sentences Vx3yP(x, y) and y\xP(x, y). Are these sentences true or false under the interpretation where x and y range over the positive integers and P(x, y) is "x divides y"? Vx³yP(x, y) is true, Vxy(x, y) is true, Vx³yP(x, y) is false, Vx³yP(x, y) is false, yvxP(x, y) is true yxP(x, y) is false y\xP(x, y) is true yvxP(x, y) is false
Transcribed Image Text:Consider the sentences Vx3yP(x, y) and y\xP(x, y). Are these sentences true or false under the interpretation where x and y range over the positive integers and P(x, y) is "x divides y"? Vx³yP(x, y) is true, Vxy(x, y) is true, Vx³yP(x, y) is false, Vx³yP(x, y) is false, yvxP(x, y) is true yxP(x, y) is false y\xP(x, y) is true yvxP(x, y) is false
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