Question

name
algebra 2b lep 4
comment:
lep checkpoint
probability
assessment lep checkpoint
complete the following problems. show all your work. you will need a scientific calculator. simplify or
write your answer as a percent where appropriate.
learning goal from lesson 19.1
how i did (circle one)
i can describe subsets of a sample space in terms of outcomes, unions,
i got it! im still learning it.
intersections, and complements.

1. match each description to the corresponding symbols from set theory. the first one is done for you. (1 point)

a. complement of set a b. union of set a and set b
~a or a^c
c. empty set d. universal set
e. set a is a subset of set b f. intersection of set a and set b
g. elements of a set h. the number of elements in set a

1. set a, set b, and set u are given. use the sets to answer the following questions. (1 point total)

a = {21,23,25,27,29}
b = {21,24,27,30}
u = {20,21,22,23,24,25,26,27,28,29,30}
a. what is a ∪ b?
a. {21,27}
b. {23,24,25,29,30}
c. {21,23,24,25,27,29,30}
b. what is a ∩ b?
a. {21,27}
b. {23,24,25,29,30}
c. {21,23,24,25,27,29,30}
c. what is a^c?
a. {21,24,27,30}
b. {20,22,23,25,26,28,29}
c. {20,22,24,26,28,30}
d. what is b^c?
a. {21,23,25,27,29}
b. {20,22,24,26,28,30}
c. {20,22,23,25,26,28,29}
e. what is n(a)? f. what is n(b)?

Explanation:

Step1: Find \(A\cup B\)

The union of two sets \(A\) and \(B\) is the set of all elements that are in \(A\) or in \(B\).
\(A = \{21,23,25,27,29\}\), \(B=\{21,24,27,30\}\)
\(A\cup B=\{21,23,24,25,27,29,30\}\)

Step2: Find \(A\cap B\)

The intersection of two sets \(A\) and \(B\) is the set of all elements that are in both \(A\) and \(B\).
\(A\cap B = \{21,27\}\)

Step3: Find \(A^{c}\)

The complement of set \(A\), \(A^{c}=U - A\), where \(U=\{20,21,22,23,24,25,26,27,28,29,30\}\)
\(A^{c}=\{20,22,24,26,28,30\}\)

Step4: Find \(B^{c}\)

The complement of set \(B\), \(B^{c}=U - B\)
\(B^{c}=\{20,22,23,25,26,28,29\}\)

Step5: Find \(n(A)\)

\(n(A)\) is the number of elements in set \(A\). Since \(A = \{21,23,25,27,29\}\), \(n(A)=5\)

Step6: Find \(n(B)\)

\(n(B)\) is the number of elements in set \(B\). Since \(B=\{21,24,27,30\}\), \(n(B) = 4\)

Answer:

a. C. \(\{21,23,24,25,27,29,30\}\)
b. A. \(\{21,27\}\)
c. C. \(\{20,22,24,26,28,30\}\)
d. C. \(\{20,22,23,25,26,28,29\}\)
e. \(5\)
f. \(4\)