do 4,5,6 Let A = {1,2,3) and B = {a,b). 1. Is the ordered pair (3.a)...
Let n > 1, and let S = {1, 2, 3}" (the cartesian product of {1,2,3} n times). (a) What is Sl? Give a brief explanation. (b) For 0 <k <n, let T be the set of all elements of S with exactly k occurrences of 3's. Determine |Tx I, and prove it using a bijection. In your solution, you need to define a set Ax that involves subsets and/or cartesian products with known cardinalities. Then clearly define your bijection...
Let S be the set of distinct ordered triples comprised of the numbers 1, 2, 3, 4. To say that the triple is distinct means that no number occurs twice in the triple. To say that the triple is ordered means that two triples in which the same numbers appear in a different order are considered to be different triples. Some of the elements of S are: 1,2,3), (1,2,4), (3,2,1), (3,2,4), (4,2,1), (4,3,2) We wish to list all of the...
#2 3.6 Cartesian Products. Direct Products (ii) List the six ordered pairs of T X S. (iii) Does S XT=TX S for these sets S and T? 2. Explain why SXT=T S if and only if S = T, S Ø , or T =%. 3. How many elements are there in S T when S has m elements and ments? 4. Describe a bijection from (s x T) * U to S x ( T U ). 5. Let...
cept of a randon PROBLEMS 1.1-1. Specify the following sets by the rule method. A= (1,2,3), B = (8, 10, 12. 14), C (1, 3, 5, 7,... 1.1-2. Use the tabular method to specify a class of sets for the sets of Problem 1.1-1. uncountable, or finite or infinite. A (1), B= (x= 1}, C ={0 < integers), D = (children in public school No. 5), E={girls in public school No. 5), F = {girls in class in public 1.1-3....
JU, I - 4, y = -1 = (4, -1) The solution is the ordered pair (4, -1) Check by substituting these values into the original equations. EXERCISES Use the substitution method to solve each system of linear equations. 1) x = y + 3 x + 7 = 2y 2) y = 2x 3x + y = 10 3) y = 3x 5x - 2y = 1 4) y = x + 4 3x + y = 16 5)...
5-13 please Homework on sets 1. let the universe be the set U (1,23. .,1.0), A (147,10), B- (1,2 list the elements for the following sets. a. B'nt C-A) b. B-A c. ΒΔΑ 2. Show that A (3,2,1] and B (1,2,3) are equal 3. Show that X Ixe Rand x > 0 and x < 3j and ( 1,2) are equal. 5. Use a Ven diagram and shade the given set. (cnA)-(B-Arnc) Show that A (x| x3-2x2-x+2 O) is not...
Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} be the universal set. Consider the two subsets A = {0, 2, 4, 6, 8} and B = {0,3,6,9}. Use the roster method to write each of the following sets (a) AUB. (b) An B. (c) AC. (d) (AUB) – AC
Let R be the relation on the set {1, 2, 3} containing the ordered pairs (1, 1), (1, 2), (2, 3), (3, 1). Find a) R 2 b) R 3 c) R 4 d) R 5 Consider the same relation R as above. List all walks in R staring from node 3 that correspond to the edges in a) R 2 b) R 3
Question 5+ The income and education level of each person on the electoral roll for Queanberra is recorded as a pair (x, y) E 1,2,3)2, where 1 stands for low, 2 for average, and 3 for high, e.g. (2,3) represents a highly educated person with average income. Let S denote the set of all people on the Queanberra electoral roll, and define random variables X, Y : S → { 1,2,3) by X(s),y(s) are the income and educational levels of...
Question 5+ The income and education level of each person on the electoral roll for Queanberra is recorded as a pair (x, y) E 1,2,3)2, where 1 stands for low, 2 for average, and 3 for high, e.g. (2,3) represents a highly educated person with average income. Let S denote the set of all people on the Queanberra electoral roll, and define random variables X, Y : S → { 1,2,3) by X(s),y(s) are the income and educational levels of...