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Assignment 1 Solutions
CS2102, Fall 2009
1.
(5.1, 1)
Answer: A and C are equal, B and D are equal
Explanation: Two sets are equal if they are both subsets of each other. Every
element of A is an element of C, so A is a subset of C. Every element of C is an
element of A, so C is a subset of A. Therefore the sets are equal. The same applies
for sets B and D.
2.
(5.1, 2)
Answer: 4 is not equal to {4}
Explanation: 4 is a number. {4} is a set which contains the element 4. The two are
not of the same type, and thus it does not make sense to say they are equal.
3.
(5.1, 5c)
Answer:
ø is an element of { ø }
Explanation: {
ø} contains one element, the empty set. Therefore, ø, the empty
set, is an element of {
ø }
4.
(5.1, 8c, d, e, h, j)
Answer: 8c. {2} is not an element of {1, 2}.
Explanation: {2} is a set that contains the element 2. In the set {1, 2}, there is no
element that is a set. Therefore, {2} can not be an element of {1, 2}. If the
question had asked if {2} is an element of {1, {2}}, or if 2 is an element of {1, 2},
the answer would have been yes.
Answer: 8d. {3} is an element of {1, {2}, {3}}.
Explanation: {1, {2}, {3}} has three elements: the number 1, a set that contains
the number 2, and a set that contains the number 3. Therefore {3}, a set that
contains the number 3, is an element of the set.
Answer: 8e. 1 is an element of {1}.
Explanation: {1} is a set with a single element, the number 1. Therefore, 1 is an
element of the set.