Please detail all your answers 2. Consider the function f : {1, 2, 3, 4, 5}...
Please detail all your answers
2. Consider the function f : {1, 2, 3, 4, 5} → {1, 2, 3, 4} given by the table below: (15 points) x 1 2 3 4 5 f (x) 3 2 4 1 2 (a) Is f injective? Explain.
(b) Is f surjective? Explain.
(c) Write the function using two-line notation.
5. In the game of Hearts, four players are each dealt 13 cards from a deck of 52. Is this a function? If so, what sets make up the domain and codomain, and is the function injective, surjective, bijective, or neither? (25 points)
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Please detail all your answers
2. Consider the function f : {1, 2, 3, 4, 5}...
Answer the questions in the space provided below. 1. The definition of a function f: X...
Answer the questions in the space provided below. 1. The definition of a function f: X + Y is as a certain subset of the product X x Y. Let f: N + N be the function defined by the equation f(n) = n2. For each pair (x, y) listed below, determine whether or not (x,y) ef. a) (2,4) b) (5, 23) c) (1,1) d) (-3,9) 2. For each function defined below, state whether it is injective (one-to-one) and whether...
Discrete Math The following functions all have domain {1,2,3,4,5} and codomain 1,2,3. For each, determine whether...
Discrete Math
The following functions all have domain {1,2,3,4,5} and codomain 1,2,3. For each, determine whether it is jective, bijective, 3. (only) injective, (only) sur neither injective nor surjective. or 1 2 4 5 3 (a) f 1 2 1 2 1 2 3 45 1 (b) f 1 2 1 2 3 if x 3 (c) f(x) if x >3 x -3
Let X = {0, 1, 2} and Y = {0,1,2}. Now we define f={(0,1),(1,0),(2,1)] Please enter...
Let X = {0, 1, 2} and Y = {0,1,2}. Now we define f={(0,1),(1,0),(2,1)] Please enter your answer as a sum of the following numbers (they are not mutually exclusive): • 1 ifff is a function f : X Y • 2 ifff is a function and it is also injective • 4ifff is a function and it is also surjective This means that your answer can be 0 (not a function), 1 (a function but neither injective or surjective)....
Question 2 [20 marks A casino is analysing a poker game where 3 cards are dealt...
Question 2 [20 marks A casino is analysing a poker game where 3 cards are dealt to the table by the dealer and two to a player, from a standard deck of 52 cards. Suppose 2 of the 3 cards on the table are Hearts and the player is holding 2 Hearts in his hand. The dealer's next action is to deal two more cards from the deck to the table. The player is interested in getting a flush which...
Say whether the following function is injective, surjective, bijective, or none of the above (note: you...
Say whether the following function is injective, surjective, bijective, or none of the above (note: you can only select one option): Domain: A= = {1,2,3,4,5,6} Codomain: B = {u, V, W, X, y, z} f = {(3,w), (4,2), (1,y), (6,w), (5x), (2,u)} O Bijective O Surjective Injective O None
#4 ,0, C, d, e, f,g, h}. (a) Using these elements, construct two sets A and...
#4
,0, C, d, e, f,g, h}. (a) Using these elements, construct two sets A and B satisfying | A=5, |B| = 4 and |An Bl 2 (b) Using the sets you chose, compute An B| 4. Let A {r : -1 < x < 1}, B = {x : -2 < x < 2}and C = {x : -2 < x < 3}, where xER. Determine whether the following statements are true or false. (a) AC B (b) C...
Given the function f : {w, x, y, z} 5 with ordering w < x < y < z and f = (4, 3, 5, 4). ...
Given the function f : {w, x, y, z} 5 with ordering w < x < y < z and f = (4, 3, 5, 4). i. Identify each of the following: domain, codomain or range, image ii. Is f one-to-one? Explain. 1 iii. Is f onto? Explain.
2. Let us construct a 36-card deck by removing all the hearts and kings out of...
2. Let us construct a 36-card deck by removing all the hearts and kings out of a standard 52-card deck. That is, we have 12 face cards (1 through 10 plus jack and queen) for each of the three remaining suits, ^, ◇, and鸁Next, deal out a total of five cards. Since players sort their hands. order doesn't m atter. (a) (9 pts) What is the probability Pth of being dealt full house (3-of-a-kind +pair)? FH (b) (10 pts) Write...
5. Let A = P(R). Define f : R → A by the formula f(x) =...
5. Let A = P(R). Define f : R → A by the formula f(x) = {y E RIy2 < x). (a) Find f(2). (b) Is f injective, surjective, both (bijective), or neither? Z given by f(u)n+l, ifn is even n - 3, if n is odd 6. Consider the function f : Z → Z given by f(n) = (a) Is f injective? Prove your answer. (b) Is f surjective? Prove your answer
10.3.1 Exercises 10.33: An ordinary function graph combines domain and range information in a single picture: we plot the ordered pair (x, f(x)). several variables we quickly run out of pictures...
10.3.1 Exercises 10.33: An ordinary function graph combines domain and range information in a single picture: we plot the ordered pair (x, f(x)). several variables we quickly run out of pictures we can draw, but there is simple alternative, which we illustrate first with an ordinary function from R to R. (This is exactly a domain-range picture, introduced in Section 1.3.) Take f(x) 2. Draw the domain of the function as a single vertical line (fair: the domain is R)....
Answer the questions in the space provided below. 1. The definition of a function f: X + Y is as a certain subset of the product X x Y. Let f: N + N be the function defined by the equation f(n) = n2. For each pair (x, y) listed below, determine whether or not (x,y) ef. a) (2,4) b) (5, 23) c) (1,1) d) (-3,9) 2. For each function defined below, state whether it is injective (one-to-one) and whether...
Discrete Math
The following functions all have domain {1,2,3,4,5} and codomain 1,2,3. For each, determine whether it is jective, bijective, 3. (only) injective, (only) sur neither injective nor surjective. or 1 2 4 5 3 (a) f 1 2 1 2 1 2 3 45 1 (b) f 1 2 1 2 3 if x 3 (c) f(x) if x >3 x -3
Let X = {0, 1, 2} and Y = {0,1,2}. Now we define f={(0,1),(1,0),(2,1)] Please enter your answer as a sum of the following numbers (they are not mutually exclusive): • 1 ifff is a function f : X Y • 2 ifff is a function and it is also injective • 4ifff is a function and it is also surjective This means that your answer can be 0 (not a function), 1 (a function but neither injective or surjective)....
Question 2 [20 marks A casino is analysing a poker game where 3 cards are dealt to the table by the dealer and two to a player, from a standard deck of 52 cards. Suppose 2 of the 3 cards on the table are Hearts and the player is holding 2 Hearts in his hand. The dealer's next action is to deal two more cards from the deck to the table. The player is interested in getting a flush which...
Say whether the following function is injective, surjective, bijective, or none of the above (note: you can only select one option): Domain: A= = {1,2,3,4,5,6} Codomain: B = {u, V, W, X, y, z} f = {(3,w), (4,2), (1,y), (6,w), (5x), (2,u)} O Bijective O Surjective Injective O None
#4
,0, C, d, e, f,g, h}. (a) Using these elements, construct two sets A and B satisfying | A=5, |B| = 4 and |An Bl 2 (b) Using the sets you chose, compute An B| 4. Let A {r : -1 < x < 1}, B = {x : -2 < x < 2}and C = {x : -2 < x < 3}, where xER. Determine whether the following statements are true or false. (a) AC B (b) C...
2. Let us construct a 36-card deck by removing all the hearts and kings out of a standard 52-card deck. That is, we have 12 face cards (1 through 10 plus jack and queen) for each of the three remaining suits, ^, ◇, and鸁Next, deal out a total of five cards. Since players sort their hands. order doesn't m atter. (a) (9 pts) What is the probability Pth of being dealt full house (3-of-a-kind +pair)? FH (b) (10 pts) Write...
5. Let A = P(R). Define f : R → A by the formula f(x) = {y E RIy2 < x). (a) Find f(2). (b) Is f injective, surjective, both (bijective), or neither? Z given by f(u)n+l, ifn is even n - 3, if n is odd 6. Consider the function f : Z → Z given by f(n) = (a) Is f injective? Prove your answer. (b) Is f surjective? Prove your answer
10.3.1 Exercises 10.33: An ordinary function graph combines domain and range information in a single picture: we plot the ordered pair (x, f(x)). several variables we quickly run out of pictures we can draw, but there is simple alternative, which we illustrate first with an ordinary function from R to R. (This is exactly a domain-range picture, introduced in Section 1.3.) Take f(x) 2. Draw the domain of the function as a single vertical line (fair: the domain is R)....
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