SECOND UNIT EXAM
1.- If S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and A= {0, 2, 4, 6, 8), B = {1, 3, 5 , 7, 9), C= (2, 3, 4, 5} and D= {1, 6, 7}, list the elements of the sets that correspond to the following events:
a) (AUC); b) (ANB); c) C; d) (CD) UB; e) (Snc); Ancn D g) P(D)
2.- A developer of a new subdivision offers potential home buyers a choice between: Tudor, rustic, colonial and traditional façade style. And between one floor, two floors and unevenness the construction plan. How many different ways can a buyer order one of these homes?
3.- In how many ways can 7 different trees be planted in a circle?
How many different permutations can be made with all the letters of the word TELEPHONY? 4.- The following is a classification, according to gender and level of education, of a random sample of
260 adults. Education: Primary 40% (45% Men, 55% Women)
Secondary 35% (28% Men, 72% Women)
University 25% (32% Men, 68% Women)
If a person is chosen at random from this group, what is the probability that: a) the person is a man, given that his education is high school? b) That the person does not have a university degree, given that she is a woman?
Accepted Solution
A:
1.a) The union of sets A and C, denoted as (AUC), is the set of elements that belong to either A or C or both. To find (AUC), we simply list out all the elements that are present in either set A or set C or both.
b) The intersection of sets A and B, denoted as (ANB), is the set of elements that belong to both set A and set B. To find (ANB), we simply list out all the elements that are present in both set A and set B.
Since there are no elements that belong to both set A and set B, (ANB) is an empty set.
c) Set C is given as {2, 3, 4, 5}.
Therefore, C = {2, 3, 4, 5}.
d) The union of sets CD and B, denoted as (CD) UB, is the set of elements that belong to either set CD or set B or both. To find (CD) UB, we simply list out all the elements that are present in either set CD or set B or both.
e) The intersection of sets S and C, denoted as Snc, is the set of elements that belong to both set S and set C. To find Snc, we simply list out all the elements that are present in both set S and set C.
f) The intersection of sets Snc and D, denoted as Snc n D, is the set of elements that belong to both set Snc and set D. To find Snc n D, we simply list out all the elements that are present in both set Snc and set D.
$$Snc n D = \{2, 3, 4, 5\} \cap \{1, 6, 7\} = \{\}$$
Since there are no elements that belong to both set Snc and set D, Snc n D is an empty set.
g) The power set of set D, denoted as P(D), is the set of all possible subsets of D, including the empty set and the set itself. To find P(D), we simply list out all possible subsets of D.