Homework Answers
![Equivalence\:class\:of\:element\:a\:is:\:\left[a\right]=\left\{x\in A:\:xRa\right\}\:,\\ \\ \:where\:A\:is\:set\:on\:which\:relation\:is\:defind.\:xRa\:mean\:x\:is\:related\:to\:a](http://img.homeworklib.com/questions/ec3a4680-18ab-11ec-b1e7-61331f0d5da3.png?x-oss-process=image/resize,w_560)
![Observe\:that\::\:\left(1,1\right)\in R\:\:\Rightarrow 1R1\:\ \ \ \ \ \& \ \ \ \ \:But\:1\:is\:not\:related\\ \:to\:any\:other\:element\:\Rightarrow \left[1\right]=\left\{1\right\}](http://img.homeworklib.com/questions/ec9a10a0-18ab-11ec-a845-e58f6e748495.png?x-oss-process=image/resize,w_560)
![Observe\:that\::\:\left(2,2\right)\:\&\:\left(2,3\right)\in R\:\ \ \Rightarrow \:2R2\:\ \ \:\&\:\ \ \ \:\:2R3\:\ \ \ \\ \:But\:1\:is\:not\:related\:to\:any\:other\:element\:\Rightarrow \left[2\right]=\left\{2,\:3\right\}](http://img.homeworklib.com/questions/ecf50960-18ab-11ec-83b0-a3dfb51bc4e1.png?x-oss-process=image/resize,w_560)
![Observe\:that\::\:\left(4,4\right)\:\&\:\left(4,5\right)\in R\:\ \ \Rightarrow \:4R4\:\ \ \:\&\:\ \ \ \:\:4R5\:\ \ \ \\ \:But\:1\:is\:not\:related\:to\:any\:other\:element\:\Rightarrow \left[4\right]=\left\{4,\:5\right\}](http://img.homeworklib.com/questions/ed409470-18ab-11ec-8733-cf60224e7044.png?x-oss-process=image/resize,w_560)
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Consider the following relation R on the set A = {1,2,3,4,5}. R= {(1, 1), (2, 2),...
Consider the following. (Assume that the dice are distinguishable and that what is observed are t...
Consider the following. (Assume that the dice are distinguishable and that what is observed are the numbers that face up.) HINT [See Examples 1-3.] Two distinguishable dice are rolled; the numbers add to 7. Describe the sample space S of the experiment. (Select all that apply.) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,7) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (2,7) (1,1) (1,2)...
Determine if {(x,y) | x divides 2-y} is an equivalence relation on {1,2,3,4,5}. List the equivalence...
Determine if {(x,y) | x divides 2-y} is an equivalence relation on {1,2,3,4,5}. List the equivalence classes Determine if {(x,y) | x and y are both even or x and y are both odd} is an equivalence relation on {1,2,3,4,5}. List the equivalence classes. Determine if {(x,y) | x and y are the same height} is an equivalence relation on all people Determine if {(x,y) | x and y have the same color hair} is an equivalence relation on all...
Calculate the probability of the following events A the first number is 2 or 3 or...
Calculate the probability of the following events A the first number is 2 or 3 or 4 E the second digit is 3 or less F the second digit is 4 or greater PIE or F) P(E and F) P(A) P( A and E) P( A and F) P( A and E)+P( Aand F) 2 Dice Sample Space 1,1 2,1 3,1 4,1 5,1 1,6 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,5 2,4 3,4 4,4...
Calculate the probability of the following events A the first number is 2 or 3 or4...
Calculate the probability of the following events A the first number is 2 or 3 or4 B P(A) P(B) P(not A) P(not B) P(A or B) the second number is 1 or 2 or 3 P(A and B) P(A given B) 2 Dice Sample Space 1,6 1,5 2,5 3,5 4,5 5,5 1,4 1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 2,6 3,6 4,6 2,4 3,4 4,4 5,4 6,4 5,6 6,5...
Iculate the probability of the foltowing events G first digit 1, 2, or 3 P(F) P(G)...
Iculate the probability of the foltowing events G first digit 1, 2, or 3 P(F) P(G) | F-sum of digits-4 P(F and G) P(F given G) P(F and G)/P(G) 2 Dice Sample Space 1,6 2,6 3,6 1,5 1,1 2,1 3,1 4,1 5,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 2,5 3,5 4,5 4,6 5,5 5,6 6,5 6,6 6,1 25/2018 HW 2- Probability 1
Calculate the probability of the following events:
Calculate the probability of the following events: C = the sum of the digits is less than or equal to 6 D = the sum of the digits is greater than or equal to 7 P(C) P(D) P(C or D) P(C and D) 2 Dice Sample Space 1,11,21,31,41,51,62,12,22,32,42,52,63,13,23,33,43,53,64,14,24,34,44,54,65,15,25,35,45,55,66,16,26,36,46,56,6
3. (a) Let R be a binary relation on the set X = {1,2,3,4,5,6,7}, defined by...
3. (a) Let R be a binary relation on the set X = {1,2,3,4,5,6,7}, defined by R= {(1,3), (2,3), (3, 4), (4,4),(4,5), (5,6), (5,7)} (1) (6 pts) Find Rk for all k = 2, 3, 4, 5,... (2) (3 pts) Find the transitive closure t(R) of R by Washall's algorithm and draw the directed graph of t(R).
An experiment consists of rolling two fair dice and adding the dots on the two sides...
An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space provided below and assuming each simple event is as likely as any other, find the probability that the sum of the dots is not 2 or 8. 1 5 (1,5) First Die (1,1) 2 (2.1) (3,1) 4 (4.1) (5,1) 6 (61) 2 (1,2) (2.2) (3,2) (4,2) (5,2) (6,2) لا لا ، الا ان Second Die 3 4 (1,3)...
QUESTION 30 Let R be the relation on the set A={1,2,3,4,5} given by R={(x,y): y=x+2}. What...
QUESTION 30 Let R be the relation on the set A={1,2,3,4,5} given by R={(x,y): y=x+2}. What is the size of RoR? QUESTION 31 How many relations on the set {4,5} are reflexive? QUESTION 32 How many relations on the set {4,5} are not reflexive?
10. TRUE or FALSE: Write TRUE if the statement is always true; otherwise, write FALSE. _a....
10. TRUE or FALSE: Write TRUE if the statement is always true; otherwise, write FALSE. _a. {0} c{{0}, {{0}}} _b. Ø $ ({1, 2}), the power set of {1,2} c. If5<3 then 8 is an odd integer. d. The relation R = {(a,b), (b,a)} is symmetric but not transitive on the set X = {a,b}. e. The relation {(1,2), (2,2)} is a function from A={1,2} to B={1,2,3} _f. If the equivalence relation R = {(1,1), (2,2), (3,3), (4,4), (1,3), (3,1),...
Calculate the probability of the following events A the first number is 2 or 3 or 4 E the second digit is 3 or less F the second digit is 4 or greater PIE or F) P(E and F) P(A) P( A and E) P( A and F) P( A and E)+P( Aand F) 2 Dice Sample Space 1,1 2,1 3,1 4,1 5,1 1,6 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,5 2,4 3,4 4,4...
Calculate the probability of the following events A the first number is 2 or 3 or4 B P(A) P(B) P(not A) P(not B) P(A or B) the second number is 1 or 2 or 3 P(A and B) P(A given B) 2 Dice Sample Space 1,6 1,5 2,5 3,5 4,5 5,5 1,4 1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 2,6 3,6 4,6 2,4 3,4 4,4 5,4 6,4 5,6 6,5...
Iculate the probability of the foltowing events G first digit 1, 2, or 3 P(F) P(G) | F-sum of digits-4 P(F and G) P(F given G) P(F and G)/P(G) 2 Dice Sample Space 1,6 2,6 3,6 1,5 1,1 2,1 3,1 4,1 5,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 2,5 3,5 4,5 4,6 5,5 5,6 6,5 6,6 6,1 25/2018 HW 2- Probability 1
3. (a) Let R be a binary relation on the set X = {1,2,3,4,5,6,7}, defined by R= {(1,3), (2,3), (3, 4), (4,4),(4,5), (5,6), (5,7)} (1) (6 pts) Find Rk for all k = 2, 3, 4, 5,... (2) (3 pts) Find the transitive closure t(R) of R by Washall's algorithm and draw the directed graph of t(R).
An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space provided below and assuming each simple event is as likely as any other, find the probability that the sum of the dots is not 2 or 8. 1 5 (1,5) First Die (1,1) 2 (2.1) (3,1) 4 (4.1) (5,1) 6 (61) 2 (1,2) (2.2) (3,2) (4,2) (5,2) (6,2) لا لا ، الا ان Second Die 3 4 (1,3)...
QUESTION 30 Let R be the relation on the set A={1,2,3,4,5} given by R={(x,y): y=x+2}. What is the size of RoR? QUESTION 31 How many relations on the set {4,5} are reflexive? QUESTION 32 How many relations on the set {4,5} are not reflexive?
10. TRUE or FALSE: Write TRUE if the statement is always true; otherwise, write FALSE. _a. {0} c{{0}, {{0}}} _b. Ø $ ({1, 2}), the power set of {1,2} c. If5<3 then 8 is an odd integer. d. The relation R = {(a,b), (b,a)} is symmetric but not transitive on the set X = {a,b}. e. The relation {(1,2), (2,2)} is a function from A={1,2} to B={1,2,3} _f. If the equivalence relation R = {(1,1), (2,2), (3,3), (4,4), (1,3), (3,1),...
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