Exam (elaborations)
COS1501 EXAM PACK 2025 {DETAILED QUESTIONS AND ANSWERS }
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- University Of South Africa
COS1501 EXAM PACK 2025 {DETAILED QUESTIONS AND ANSWERS }
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,Question 1The set of all non-negative integers x less than 16 such that x2 is an
even integer can be described as the set:
1. {x x Z≥, x < 16, x2 = 2k for some k Z}
2. {x x Z≥, x < 16, x2 = 2k for some k Z+}
3. {0, 2, 4, 16, 36, 64, 100, 144, 196}
4. {0, 2, 4}
(Note: The required set must include as elements all non-negative
integers x such that all the requirements for the set are met.)
Question 2
{x x Z, 0 x < 8} {x x R, 4 x < 16} is the set:
1. {x x R, 4 x < 8}
2. {x x Z, 0 x 8}
3. {x x Z, 0 x 16}
4. {4, 5, 6, 7}
Consider the following sets, where U represents a universal set:
U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}}
C = {2, {1}, {2}}.
(Hint: U has 5 elements namely 1, 2, {1}, {2}, and {1, 2}, A has 3
elements, B has 2 elements and C has 3 elements. List the elements
of A, B and C before answering the questions.)
Questions 3 to 10 are based on the sets defined above.
NOTE: The Venn diagrams in study unit 4 will help you to
understand the definitions in study unit 3.
Question 3
A B is the set:
1. {1, 2, {1}, {1, 2}}
2. {1, 2, {1, 2}}
3. {{1}, {1, 2}}
,4. {{1}}
Q
u
e
s
t
i
o
n
4
A
C
i
s
t
h
e
s
e
t
:
1. {2, {1, 2}}
2. {1, 2, {1}}
3. {2, {1}, {2}}
4. {2, {1}}
Question 5
A – B is the set:
1
.
{
1
,
2
}
2
.
, {
1
,
{
1
,
2
}
}
3. {}
4. {{1, 2}}
Q
u
e
s
t
i
o
n
6
B
+
C
i
s
t
h
e
s
e
t
:
1. {{1, 2}}
2. {{1}, {2}}
3. {2, {2}, {1, 2}}
4. {2, {1}, {2}, {1, 2}}
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