Five Discrete math questions
vhramu223
quiz_3.docx
1. Let A={2,5,7}, and let ℘(A) represent the power set of A . Then the cardinality of the set ℘(A) is equal to what?
2. Let S=A×BS=A×B where A={2,3,4}A={2,3,4} and B={3,5}B={3,5}.
Which of the following statements are true?
a. {(4,5)}∈S{(4,5)}∈S
b. ∅⊂S∅⊂S
c. (5,4)∈S(5,4)∈S
d. A⊂SA⊂S
e. {(4,5),(2,3)}⊂S{(4,5),(2,3)}⊂S
f. (4,5)∈S
3. Which of the sets below are partitions of the set A={2,3,4,5,6,7,8,9}A={2,3,4,5,6,7,8,9}?
This question penalizes wrong answers, so guessing is inadvisable.
a. {{2,3},{4,5},{7,8},{9}}{{2,3},{4,5},{7,8},{9}}
b. {{3,4},{2,5,7},{6,8,9}}{{3,4},{2,5,7},{6,8,9}}
c. {{2,3,4},{5,6,7,8,9}}{{2,3,4},{5,6,7,8,9}}
d. {{2,3},{4,5,6},{7,8,9},{ }}{{2,3},{4,5,6},{7,8,9},{ }}
e. {{2,3,4},{5,6,7},{4,6,8,9}}{{2,3,4},{5,6,7},{4,6,8,9}}
4. A grandmother is cleaning out her garage and finds 6 items that she no longer wants to store. She has two charities that she likes to donate to, so she is going to put the 6 items into two boxes. She wants to give at least one item to each charity. She does not care which charity gets which items, so the boxes are not labeled.
How many different ways are there for her to place the 6 items into 2 unlabeled boxes?
For example {{1,2,3,4},{5,6}} is one way and {{1,2,4,5},{3,6}} is another.
But {{1,2,3,4,6},{5}} is the same as {{5},{1,2,3,4,6}}.
f. 30
g. 31
h. 36
i. 11
j. 15
k. 12
5. Consider the following subsets of NN:
A={x|(∃y)(y∈NA={x|(∃y)(y∈N and x=3y)}x=3y)}
B={x|(∃y)(y∈NB={x|(∃y)(y∈N and x=2y)}x=2y)}
C={x|x∈NC={x|x∈N and |x|≤10}|x|≤10}
Which of the following statement(s) are true about the set A∩B∩CA∩B∩C?
This question penalizes wrong answers, so guess cautiously.
l. {∅}⊆A∩B∩C{∅}⊆A∩B∩C
m. 6∈A∩B∩C6∈A∩B∩C
n. 12∈A∩B∩C12∈A∩B∩C
o. ∅∈A∩B∩C∅∈A∩B∩C
p. {12}∈A∩B∩C{12}∈A∩B∩C
q. {6}⊆A∩B∩C{6}⊆A∩B∩C
