Logic question Given (∀ x)(∃ y)(P(x,y)) I need to provide an example that is true and one that is false. For true Domain is all integers x + y = 0 If y is -x, this is true. False Domain is all real numbers x = y^2 If x = -1, y^2 can never be -1. I think these are ok but unsure. Thank you

Database System Concepts
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ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Logic question Given (∀ x)(∃ y)(P(x,y)) I need to provide an example that is true and one that is false. For true Domain is all integers x + y = 0 If y is -x, this is true. False Domain is all real numbers x = y^2 If x = -1, y^2 can never be -1. I think these are ok but unsure. Thank you
Expert Solution
Step 1

Your examples are correct!

For the true example, if we let the domain be all integers, and P(x,y) is defined as x + y = 0, then we can choose y to be -x for any value of x, and we will have P(x,y) true for all x in the domain.

For example, P(1,-1) is true because 1 + (-1) = 0, and P(2,-2) is also true because 2 + (-2) = 0.

 

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