I. Draw the directed graph and list the set of ordered pair of R, of the following. 1. If X={1,2,3,4} and Y={6,8,10} then define the relation R from X to Y such that elements X when squared are less than elements in Y. 2. If X=(1,3,4,6,7} and Y={1,2,3,5} then define the relation R from X to Y such that the sum of an element in X plus an element in Y is odd. II. Consider the following relations. A = {1, 2, 3) 1. Give all relations RCA x A, where A x A = {: x & A, y ɛ A}. 2. Number of tuples in A x A = |A|x Al is equal to. 3. All possible of subsets of A x A:, what is the total number? 4. R₁ & AXA: x=y} 5. R₂= {x,y> & AxA:x≤y} 6. R. (x, y> & AxA:x & AXA: x+y≤3} 8. R₁ {} 9. Given set A = {0, 1, 2, 3, 4); what is the set B = {a & A: a<0}? 10. If & R; & R; & R; Basis <0, 0, 0> & R; a. x <5, 4, 9> & R 11. If & R then & R; Basis <0,0> & R; x = <10, 20>
I. Draw the directed graph and list the set of ordered pair of R, of the following. 1. If X={1,2,3,4} and Y={6,8,10} then define the relation R from X to Y such that elements X when squared are less than elements in Y. 2. If X=(1,3,4,6,7} and Y={1,2,3,5} then define the relation R from X to Y such that the sum of an element in X plus an element in Y is odd. II. Consider the following relations. A = {1, 2, 3) 1. Give all relations RCA x A, where A x A = {: x & A, y ɛ A}. 2. Number of tuples in A x A = |A|x Al is equal to. 3. All possible of subsets of A x A:, what is the total number? 4. R₁ & AXA: x=y} 5. R₂= {x,y> & AxA:x≤y} 6. R. (x, y> & AxA:x & AXA: x+y≤3} 8. R₁ {} 9. Given set A = {0, 1, 2, 3, 4); what is the set B = {a & A: a<0}? 10. If & R; & R; & R; Basis <0, 0, 0> & R; a. x <5, 4, 9> & R 11. If & R then & R; Basis <0,0> & R; x = <10, 20>
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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Transcribed Image Text:I. Draw the directed graph and list the set of ordered pair of R, of the following.
1. If X={1,2,3,4} and Y={6,8,10} then define the relation R from X to Y such that elements X when
squared are less than elements in Y.
2. If X={1,3,4,6,7} and Y={1,2,3,5} then define the relation R from X to Y such that the sum of an
element in X plus an element in Y is odd.
II. Consider the following relations.
A = {1, 2, 3}
1. Give all relations RCA x A, where A x A = {<x, y>: x & A, y & A}.
2.
Number of tuples in A x A = |A| x |A| is equal to.
3. All possible of subsets of A x A:, what is the total number?
4. R₁ = {<x, y> & AXA: x=y}
5.
R₂ = {x,y> & AxA:x≤y}
6. R₂ = {<x, y> & AxA:x<y}
7. R.= {x,y> & AxA: x+y≤3}
8. R₁ = {}
9. Given set A = {0, 1, 2, 3, 4); what is the set B = {a & A: a<0}?
10. If <x, y, z> & R; <x + 1, y, z + 1> & R; <x, y + 1, z+1> & R; Basis <0, 0, 0> & R;
a. x=<5, 4, 9> & R
11. If<x, y> & R then <x+1, y +2> & R; Basis <0,0> & R; x = <10, 20>
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