National University of Lesotho
Department of Mathematics and Computer Science
M1503
Tutorial 1
Sept 2023
1. Describe (in words or mathematical notation) the given sets below.
(a) A = {2, 4, 6, 8, 10}
(c) C = {1, 4, 9, 16, 25, 36}
(b) B = {2, 4, 6, 8, 10, . . .}
(d) E = {a, b, c, d}
2. For each of the sets below, tell which is finite and which is infinite. For the finite sets, tell
which are equivalent and which are equal.
(a) The set of the first two odd counting numbers
(b) The set of all odd counting numbers less than 6
(c) The set of distinct letters in the word ”qomoqomong”
(d) The set of all odd counting numbers
(e) The set of all first year students at NUL this year.
(f) The set whose elements are 1 and 3.
3. If E = {0, 1, 2, ..., 9}, A = {0, 1, 2, 3, 4, 5}, B = {2, 3, 4, 5}, C = {4, 5, 6, 7}, and D = {6, 7, 8, 9},
find
(a) A ∪ B
(f) B ∩ C
(k) B c ∪ Dc
(b) B ∪ C
(g) A ∪ ∅
(l) (A ∪ B)c
(c) C ∩ D
(h) B ∩ ∅
(d) D ∪ A
(i) C ∪ E
(e) B ∩ D
(j) D ∩ E
(m) (B ∩ D)c
(n) (E ∪ ∅)c
4. In a class of 150 students, each of whom take M1503 or CS1311, 130 take M1503 and 125 take
CS1311. How many students take both? (Hint: use venn diagrams)
5. Given that there are 60 students in FSS who are registered for courses and they are registered
either for ST1511, CS1311 or M1503. Of the 60, 44 are registered in ST1511, 36 registered for
CS1311 and 14 are registered for M1503. If 20 students are registered for both ST1511 and
CS1311, 10 are registered for both CS1311 and M1503, and 6 have registered for ST1511 and
M1503, how many of these 60 students are registered for the three courses.
6. List all subsets and all proper subsets of the following sets.
(a) {1}
(c) {1, 2, 3}
(b) {1, 2}
(d) {1, 2, 3, 4}
7. How many subsets and proper subsets can we get from a set with n elements?
8. If A = {1, 2, 3, 4, 5, 6} , B = {2, 3, 4} and C = {2, 4, 6} . Which of the following are true?
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(a) A ⊆ B
(d) B ⊂ C
(g) C ⊂ C
(b) A ⊂ C
(e) C ⊂ A
(h) ∅ ⊂ B
(c) B ⊆ A
(f) C ∩ B = ∅
(i) A ∪ B = A
9. Classify which subset(s) of real numbers does the following numbers belong
(a) −5
(b) 0
10
(c)
5
(d)
(e)
3
10
√
(f) π
(g) 0.9
√
(h) − 81
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10. Indicate whether each of the following statements is true or false.
(a) Every integer is a whole number
(b) Every integer is a rational number
(c) Every natural number is an irrational number
(d) Every natural number is an integer
(e) Every irrational number is a realnumber
(f) Every rational number is a real number
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