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16. (x,y)ER? :x2-x=아드{(x,y)€R? :x-1=아

16. (x,y)ER? :x2-x=아드{(x,y)€R? :x-1=아

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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15 Power Sets This is a subset CSR2. Likewise the graph of a function y = f(x) is a set of points G = {(x,f(x)) : x € R}, and G S R². Surely sets such as C and G are more easily understood or visualized when regarded as subsets of R2. Mathematics is filled with such instances where it is important to regard ng elemene one set as a subset of another. valld slete Exercises for Section 1.3 A. List all the subsets of the following sets. 1. {1,2,3,4} ② {1,2,마} 3. {{R}} 5. {마} 6. {R,Q,N} 7. {R,{Q,N}} B){{0, 1}, {0, 1, {2}}, {아} fallowing 4. Ø int dlement B. Write out the following sets by listing their elements between braces. 9. {X:Xs{3,2,a} and |X|= 2} 10. {X CN:|X|< 1} 11. {X:Xs{3,2,a} and |X| = 4} 12. {X :X < {3,2,a} and X|= 1} dlement 15. {x.y)ER? :x-1=아드{(x.y)eR° :x2-x=아 16. (x,y)eR? :22-x=아드{(x,y)€R? :x-1=아} C. Decide if the following statements are true or false. Explain. 13. R° CR3 14. R CR3 mleting cntain 1.4 Power Sets Given a set, you can form a new set with the power set operation. Definition 1.4 If A is a set, the power set of A is another set, denoted as P(A) and defined to be the set of all subsets of A. In symbols, P(A)= {X:XSA}. For example, suppose A = {1,2,3}. The power set of A is the set of all subsets of A. We learned how to find these subsets in the previous section, and they are {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3} and {1,2,3}. Therefore the power set of A is P(A) = D3{0, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}}. Ø, As we saw in the previous section, if a finite set A has n elements, then it has 2" subsets, and thus its power set has 2" elements. he h u
Transcribed Image Text:15 Power Sets This is a subset CSR2. Likewise the graph of a function y = f(x) is a set of points G = {(x,f(x)) : x € R}, and G S R². Surely sets such as C and G are more easily understood or visualized when regarded as subsets of R2. Mathematics is filled with such instances where it is important to regard ng elemene one set as a subset of another. valld slete Exercises for Section 1.3 A. List all the subsets of the following sets. 1. {1,2,3,4} ② {1,2,마} 3. {{R}} 5. {마} 6. {R,Q,N} 7. {R,{Q,N}} B){{0, 1}, {0, 1, {2}}, {아} fallowing 4. Ø int dlement B. Write out the following sets by listing their elements between braces. 9. {X:Xs{3,2,a} and |X|= 2} 10. {X CN:|X|< 1} 11. {X:Xs{3,2,a} and |X| = 4} 12. {X :X < {3,2,a} and X|= 1} dlement 15. {x.y)ER? :x-1=아드{(x.y)eR° :x2-x=아 16. (x,y)eR? :22-x=아드{(x,y)€R? :x-1=아} C. Decide if the following statements are true or false. Explain. 13. R° CR3 14. R CR3 mleting cntain 1.4 Power Sets Given a set, you can form a new set with the power set operation. Definition 1.4 If A is a set, the power set of A is another set, denoted as P(A) and defined to be the set of all subsets of A. In symbols, P(A)= {X:XSA}. For example, suppose A = {1,2,3}. The power set of A is the set of all subsets of A. We learned how to find these subsets in the previous section, and they are {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3} and {1,2,3}. Therefore the power set of A is P(A) = D3{0, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}}. Ø, As we saw in the previous section, if a finite set A has n elements, then it has 2" subsets, and thus its power set has 2" elements. he h u
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