Sheet 1
Discrete mathematics
1) Give the set of letters in each word by listing
the elements of the set.
(a) ADDRESS
(b) TREE
Answer:
(a) { A,D, R, E,S}
(b) {T,R,E}
2) Find the set of smallest cardinality that
contains the given sets as subsets
{1, 2}, {1, 3}, 𝜑
Answer:{1, 2, 3}
3) Write the set in the form {x | P(x)}, where P(x) is
a property that describes the elements of the set
(a) {a, e, i, o, u}
(b) {-2, -1, 0, 1, 2}
(c) {1,2,3}
Answer:
(a) {x | x is a vowel}
(b) {x | x ∈ Z and x2 < 5}
(C ) {x | x is a positive integer and x2 < 16}
4) Let A = {3, 2, R, Z}. Identify each of the following
as true or false.
(a) Z ϵ A
(b) 5 ϵ A
(c) C A
Answer:
(a) True
(a) False
(b) True
5) Let A = {1, 2, 5, 8, 11}. Identify each of the
following as true or false.
(a) {5, 1} A
(b) {8, 1} A
(c) {1, 8, 2, 11, 5} A
(d) 𝜑 A
(e) {1, 6} A
(f) {2} A
(g) {3} A
(h) A {11, 2, 5, 1, 8, 4}
Answer:
(a) True
(b) False
(c)False
(d) True
(e) True
(f) True
(g) True
(h) True
6) Let U = {0,1,2,3,4,5,6,7}, A = {1,2,3,6}, B = {2,3,4,5}, C =
{0,2,3,7}, and D = {3,5,7}.
1. Compute
(a) A B
(d) B ∩ D
(g) A
Answer:
(a) {1,2,3,4,5,6}
(c) {2,3}
(e) {1,4,5,6}
(g) {1,2,3,6}
(i) {1,6,0,7}
(b) B C
(e) (A B) – C
(h) A ⨁ B
(c) A ∩ C
(f) A – B
(i) A⨁ C
(b) {0,2,3,4,5,7}
(d) {3,5}
(f) {1,6}
(h) {1,6,4,5}
7) Let U = {0,1,2,3,4,5,6,7}, A = {1,2,3,6},
B = {2,3,4,5}, C = {0,2,3,7}, and D = {3,5,7}.
Compute
(a) A B C
(b) A ∩ B ∩ C (c) A ∩ (B C)
(d) (A B) ∩ C (e) A B
(f) A ∩ B
Answer:
(a) {0,1,2,3,4,5,6,7}
(c) {2,3}
(e) { 0,7}
(b) {2,3}
(d) {2,3}
(f) {0,1,4,5,6,7}
Assignment
1 . List the members of these sets.
a) {x I x is a real number such that x2 =1}
b) {x I x is a positive integer less than 12 }
c) { x I x is the square of an integer and x < 1 00}
2) Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 4, 6,8},
B = {2, 4, 5, 9}, C = {x | x is a positive integer and
x2 16}
Compute:
(a) A B
(b) A C
(c) B C
(d) A C
(e) B C
3) Let U = {1,2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 7},
B = {4, 3, 5, 6}, C = {1, 2, 6}, and D = {3,5,7}.
Compute
(a) A B
(b) A C
(c) (A B) – C
(d) A
(e) A B