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
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 13EQ
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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}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a11a7d4-7053-4f89-b3df-cd695c20ba0b%2F1f8002ef-a34c-418f-845a-3c657b94489a%2Fe1ka4dn_processed.jpeg&w=3840&q=75)
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}
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