ADDITIONAL EXERCISES: These exercises are NOT REQUIRED to be submitted. However, you can try these exercises for you to experience first hand the process in answering these set of exercises. 1. Let A = {blue, apple} and B = {banana, mango, grapes. durian}. Define relation M from B to A as follows For all (x,y) E Bx A, (x,y) E M means that the second component is a color. List down the elements of M. Is relation M a function? Why or why not? 2. Let C = {1, 2, 3, 4} and D = {1, a, 2, b, 3} Define relation N from D to C as follows For all (x,y) E D x C, (x,y) EN means that x is equal to y. List down the elements of N. Is relation N a function? Why or why not? 3. Let C= {1,2,3} Define relation O from C to C as follows For all (x,y) E C x C, (x,y) E O means that x is less than or equal y. List down the elements of O. Is relation O a function? Why or why not? 4. Determine whether the operation defined per each item is a binary operation or not. a. Let GE N = (1, 2, 3, 4, 5, ...}. (set of all counting numbers) Define * on G, for any a,b E G, a * b = a + 2b. b. Let H E Z = {..., -5, -4, -3, -2, -1} (set of all negative integers) Define * on H, for any a,b E H, a *b = a - b.
ADDITIONAL EXERCISES: These exercises are NOT REQUIRED to be submitted. However, you can try these exercises for you to experience first hand the process in answering these set of exercises. 1. Let A = {blue, apple} and B = {banana, mango, grapes. durian}. Define relation M from B to A as follows For all (x,y) E Bx A, (x,y) E M means that the second component is a color. List down the elements of M. Is relation M a function? Why or why not? 2. Let C = {1, 2, 3, 4} and D = {1, a, 2, b, 3} Define relation N from D to C as follows For all (x,y) E D x C, (x,y) EN means that x is equal to y. List down the elements of N. Is relation N a function? Why or why not? 3. Let C= {1,2,3} Define relation O from C to C as follows For all (x,y) E C x C, (x,y) E O means that x is less than or equal y. List down the elements of O. Is relation O a function? Why or why not? 4. Determine whether the operation defined per each item is a binary operation or not. a. Let GE N = (1, 2, 3, 4, 5, ...}. (set of all counting numbers) Define * on G, for any a,b E G, a * b = a + 2b. b. Let H E Z = {..., -5, -4, -3, -2, -1} (set of all negative integers) Define * on H, for any a,b E H, a *b = a - b.
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:ADDITIONAL EXERCISES:
These exercises are NOT REQUIRED to be submitted. However, you can try these exercises for
you to experience first hand the process in answering these set of exercises.
1. Let A = {blue, apple} and B = {banana, mango, grapes. durian}.
Define relation M from B to A as follows
For all (x,y) E B x A, (x,y) E M means that the second component is a color.
List down the elements of M.
Is relation M a function? Why or why not?
2. Let C = {1, 2, 3, 4} and D = {1, a, 2, b, 3}
Define relation N from D to C as follows
For all (x,y) E D x C, (x,y) E N means that x is equal to y.
List down the elements of N.
Is relation N a function? Why or why not?
3. Let C= {1,2,3}
Define relation O from C to C as follows
For all (x.y) E C x C, (x,y) E O means that x is less than or equal y.
List down the elements of O.
Is relation O a function? Why or why not?
4. Determine whether the operation defined per each item is a binary operation or not.
a. Let GE N= {1, 2, 3, 4, 5, ..}. (set of all counting numbers)
Define * on G, for any a,b E G, a * b = a + 2b.
b. Let H E Z' = {... , -5, -4, -3, -2, -1} (set of all negative integers)
Define * on H, for any a,b E H, a * b = a - b.
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