How many ordered pairs (A, B), where A, B are subsets of {1 , 2, 3, 4, 5} have:
|A ∩ B| = 1
Where A ∩ B= {1} => 3^4 = 81
Solution
Explanation
How many ordered pairs (A,B), where A, B are subsets of {1,2,3,4,5} have: |A∩B|=1
2. Given the set S-ta,b,c,d,e,f,g,h) a) How many subsets does S have? b) How many subsets have exactly 5 elements? c) A subset is randomly chosen for the collection of all possible a) b) c) subsets. What is the probability that it contains exactly 3 elements? d) A subset is chosen at random from all the subsets. d) What is the probability that it contains the element a?
5. Binomial Coefficients (a) How many subsets with at least 5 elements does a set with 8 elements have? n+3 (b). Find the coefficient of z" in (3-2)+ (c). How many ways are there to walk down from the top of Pascal's Triangle and end somewhere on the number 20? 5. Binomial Coefficients (a) How many subsets with at least 5 elements does a set with 8 elements have? n+3 (b). Find the coefficient of z" in (3-2)+ (c). How...
41. How many subsets does the set {a, b, c, d, e,f} have?
give three ordered pairs from the table 2.1.11 Give three ordered pairs from the table. х 1 1 4 5 6 у -3 5 -4 -8 -- 13 Name three ordered pairs that the table describes O A. (1, -1, 4).(-3,5, -4) O B. (-13, 1).(5. - 1).(-4,4) O C. (1. - 3).(-1,5),(4. - 4) Click to select your answer and then click Check Answer. All parts showing QuestUIT TUT Ti- javascript:do Exercise(14); Question 15 (0/1)
(b) Let F, G and H be the following sets of ordered pairs F {(1,1), (2, 2), (3,7), (4,1)} G {(1,1), (2, 1) (3, 2), (3,3), (4,2)} н 3 {(1,1), (2, 3), (3, 4), (4, 2)} (i) Does F define a function f :{1,2,3,4} (ii) Does G define a function g : {1,2,3,4} (iї) Does H define a function h : {1,2,3,4} —> {1, 2, 3, 4}? (iv) For those of f, g and h that are functions, write down...
Show your work, please 5. Binomial Coefficients (a). How many subsets with at least 5 elements does a set with 8 elements have? (b). Find the coefficient of 2" in (3 - 2.c)"+3 (c). How many ways are there to walk down from the top of Pascal's Triangle and end somewhere on the number 20?
How many subsets are there of 5 letters? How many contain at least one letter, but not all of the letters {a, b, c, d, e}?
Binomial Coefficients (a). How many subsets with at least 5 elements does a set with 8 elements have? (b). Find the coefficient of r" in (3 - 2.0)"+3. (c). How many ways are there to walk down from the top of Pascal's Triangle and end somewhere on the number 20?
How many anti-symmetric relations on the set A = {1, 2, 3, 4, 5, 6} contain the ordered pairs (2, 2), (3, 4) and (5, 6)?
4. One ordered pair u (V1,U2) dominates another ordered pair u-(ui,u2) iful > ข1 and U2 > Un Given a set S of ordered pairs, an ordered pair u E S is called Pareto optimal for S if there is no vES such that v dominates u. Give an efficient algorithm that takes as input a list of n ordered pairs and outputs the subset of all Pareto-optimal pairs in S. (10 points correct reasonably fast algorithm with justification, 5...