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Exercise 3 Consider the formula 3r.y.32. [P(x, y) A P(z,y) A P(1, 2) A-P(2,1)], For each of the following interpretations, is this formula true? In each case R is the relation corresponding to P. For example, in (a) below, P(x, y) is true when z

Exercise 3 Consider the formula 3r.y.32. [P(x, y) A P(z,y) A P(1, 2) A-P(2,1)], For each of the following interpretations, is this formula true? In each case R is the relation corresponding to P. For example, in (a) below, P(x, y) is true when z

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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Exercise 3 Consider the formula 3x.y.32. [P(x, y) A P(z,y) A P(x, 2)^¬P(z, x)], For each of the following interpretations, is this formula true? In each case R is the relation corresponding to P. For example, in (a) below, P(x, y) is true when a <y for integers x, y. (a) R = {(x,y) | x,y N and r<y} (b) R= {(x,x+1) | z € N} (c) R = {(x, y) | r, y eN and y = 2r or y = 2x + 1} (d) R = {(A,B) | A, BCN and AC B}
Transcribed Image Text:Exercise 3 Consider the formula 3x.y.32. [P(x, y) A P(z,y) A P(x, 2)^¬P(z, x)], For each of the following interpretations, is this formula true? In each case R is the relation corresponding to P. For example, in (a) below, P(x, y) is true when a <y for integers x, y. (a) R = {(x,y) | x,y N and r<y} (b) R= {(x,x+1) | z € N} (c) R = {(x, y) | r, y eN and y = 2r or y = 2x + 1} (d) R = {(A,B) | A, BCN and AC B}
Expert Solution
Step 1

Given:

The formula, ∃x.∃y.∃z.Px,y∧Pz,y∧Px,z∧¬Pz,x.

 

To determine:

If this formula is true for each of the following interpretations:

(a.) R=x,y|x,y∈ℕ and x<y

(b.) R=x,x+1|x∈ℕ

(c.) R=x,y|x,y∈ℕ and y=2x or y=2x+1

(d.) R=A,B|A,B⊆ℕ and A⊆B

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