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COT3100C01, Fall 2002
Assigned: 9/10/2002
S. Lang
Assignment #2 (40 pts.)
Due: 9/19 in class by 8:45 am
1.
(10 pts.) The following Venn diagram shows three sets
A
(red)
,
B
(blue)
, and
C
(green)
contained within a universe set named
U
(violet)
.
In the diagram, different subsets (regions)
are labeled by the numbers 1 through 8.
Thus, set
A
contains subsets labeled 1, 2, 4, and 5;
set
B
contains subsets labeled 2, 3, 5, and 6; set
C
contains subsets labeled 4, 5, 6, and 7; set
U
contains subsets labeled 1 through 8 (i.e., the universe).
Now, give the labels (i.e.,
numbers) of all the subsets that are contained in each of the following sets:
2.
(24 pts.) Prove each of the following statements (a) – (f), assuming the symbols
A
,
B
, and
C
represent sets contained in a universe set
U
.
You are allowed to use appropriate definitions,
and the following theorems and laws (
but
only these
) in the proof.
Be sure to
explain each
step of your proof
.
(Commutative Law)
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