COT3100C-01, Fall 2000
Assigned: 9/14/2000
S. Lang
Assignment #2 (40 pts.)
Due: 9/26, by 1:10 pm in class
1.
(6 pts.) The following Venn diagram shows three sets
A
,
B
, and
C
contained within a
universe set named
U
.
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 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.
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)
A
∪
B =
B
∪
A
,
A
∩
B
=
B
∩
A
.
(Associative Law) (