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5. Let N² = {(a,b): a, b, E N} be the set of ordered pairs of natural numbers. For example, (1.2) and (4,1) are elements of N². Define A = {(a,b) EN²: (2-a)(2+b) > 2(b-a)} Give (with proof) a description of A in roster notation (i.e. a list of elements).

5. Let N² = {(a,b): a, b, E N} be the set of ordered pairs of natural numbers. For example, (1.2) and (4,1) are elements of N². Define A = {(a,b) EN²: (2-a)(2+b) > 2(b-a)} Give (with proof) a description of A in roster notation (i.e. a list of elements).

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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5. Let N² = {(a,b): a, b, E N} be the set of ordered pairs of natural numbers. For example, (1, 2) and (4,1) are elements of N². Define A = {(a, b) = N²: (2-a)(2+b) > 2(b-a)} Give (with proof) a description of A in roster notation (i.e. a list of elements). 6. Let A = {(x,y) R²: 2-2-2y < (2-x)(1-y)}. Give (with proof) a simple description of A (your description can involve the signs of r and y). For the next two problems: Draw Venn diagrams to make a conjecture about whether the statement about arbitrary sets is true or false. Then either prove or give a counterexample (your counterexample must include specific sets-a Venn Diagram is not enough). You do not need to include the Venn diagrams in your solutions. 7. AU (B-C) = (AUB) - (AUC) 8. An (B-C)= (ANB) - (ANC)
Transcribed Image Text:5. Let N² = {(a,b): a, b, E N} be the set of ordered pairs of natural numbers. For example, (1, 2) and (4,1) are elements of N². Define A = {(a, b) = N²: (2-a)(2+b) > 2(b-a)} Give (with proof) a description of A in roster notation (i.e. a list of elements). 6. Let A = {(x,y) R²: 2-2-2y < (2-x)(1-y)}. Give (with proof) a simple description of A (your description can involve the signs of r and y). For the next two problems: Draw Venn diagrams to make a conjecture about whether the statement about arbitrary sets is true or false. Then either prove or give a counterexample (your counterexample must include specific sets-a Venn Diagram is not enough). You do not need to include the Venn diagrams in your solutions. 7. AU (B-C) = (AUB) - (AUC) 8. An (B-C)= (ANB) - (ANC)
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