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Let R₁ = {(a, b) E P2: a divides b) and R₂ = {(a, b) E P²: a is a multiple of b) where P is the set of positive integer numbers. Find a) R₁ UR₂ b) R₁NR₂ c) R₁ R₂ d) R₂\R₁

Let R₁ = {(a, b) E P2: a divides b) and R₂ = {(a, b) E P²: a is a multiple of b) where P is the set of positive integer numbers. Find a) R₁ UR₂ b) R₁NR₂ c) R₁ R₂ d) R₂\R₁

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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e Edit View History Bookmarks Profiles Tab Window Help en HW 4 fiu.instructure.com work 4 (Fall 21).pdf 30% F2 X #3 # Problem 4. Let R₁ = {(a, b) E P²: a divides b} and R₂ = {(a, b) E P²: a is a multiple of b} where P is the set of positive integer numbers. Find a) R₁ UR₂ b) R₁NR₂ c) R₁ R₂ d) R₂\R₁ Module 4 Discussion X SEP 12 Problem 5. a) Prove that the relation R on a set A is symmetric if and only if R = R-¹, where R-¹ is the inverse relation of R. b) Prove that the relation R on a set A is antisymmetric if and only if R n R-¹ is subset of the relation A= {(a, a) | a € A}. 20 F3 $ 4 000 DOO F4 % 5 Module 4 Discussion X S F5 ^ 6 MacBook Pro F6 87 & Module 4 Discussion X ◄◄ F7 * 8 ► 11 F8 tv Module 4 Discussion ►► 9 ( F9 2 Mon 8: W 1 U ZOOM F10
Transcribed Image Text:e Edit View History Bookmarks Profiles Tab Window Help en HW 4 fiu.instructure.com work 4 (Fall 21).pdf 30% F2 X #3 # Problem 4. Let R₁ = {(a, b) E P²: a divides b} and R₂ = {(a, b) E P²: a is a multiple of b} where P is the set of positive integer numbers. Find a) R₁ UR₂ b) R₁NR₂ c) R₁ R₂ d) R₂\R₁ Module 4 Discussion X SEP 12 Problem 5. a) Prove that the relation R on a set A is symmetric if and only if R = R-¹, where R-¹ is the inverse relation of R. b) Prove that the relation R on a set A is antisymmetric if and only if R n R-¹ is subset of the relation A= {(a, a) | a € A}. 20 F3 $ 4 000 DOO F4 % 5 Module 4 Discussion X S F5 ^ 6 MacBook Pro F6 87 & Module 4 Discussion X ◄◄ F7 * 8 ► 11 F8 tv Module 4 Discussion ►► 9 ( F9 2 Mon 8: W 1 U ZOOM F10
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