Exercise 3.1.2: Set membership and subsets - true or false, cont.
Use the definitions for the sets given below to determine whether each statement is true or false:
An integer x is a perfect square if there is an integer y such that x = y2.
(a)15 ⊂ A
(b){15} ⊂ A
(c) ∅ ⊂ A
(d) A ⊆ A
(e) ∅ ∈ B
(f) A is an infinite set.
(g) B is a finite set.
(h) |E| = 3
(i) |E| = |F|
Exercise 3.1.3: Subset relationships between common numerical sets.
Indicate whether the statement is true or false.
(a) Z ⊂ R
(b) Z ⊆ R
(c) Z ⊆ R+
(d) N ⊂ R
(e) Z+ ⊂ N
Exercise 3.2.1: Sets of sets - true or false.
Let X = {1, {1}, {1, 2}, 2, {3}, 4 }. Which statements are true?
(a) 2 ∈ X
(b) {2} ⊆ X
(c) {2} ∈ X
(d) 3 ∈ X
(e) {1, 2} ∈ X
(f) {1, 2} ⊆ X
(g) {2, 4} ⊆ X
(h) {2, 4} ∈ X
(i) {2, 3} ⊆ X
(j) {2, 3} ∈ X
(k) |X| = 7
Exercise 3.3.1: Unions and intersections of sets.
Define the sets A, B, C, and D as follows:
For each of the following set expressions, if the corresponding set is finite, express the set using roster notation. Otherwise, indicate that the set is infinite.
(a) A ∪ B
(b) A ∩ B
(c) A ∩ C
(d) A ∪ (B ∩ C)
(e) A ∩ B ∩ C
(f) A ∪ C
(g) (A ∪ B) ∩ C
(h) A ∪ (C ∩ D)
Exercise 3.6.1: Cartesian product of three small sets.
The sets A, B, and C are defined as follows:
Use the definitions for A, B, and C to answer the questions. Express the elements using n-tuple notation, not string notation.
(a) Write an element from the set A × B × C.
(b) Write an element from the set B × A × C.
(c) Write the set B × C using roster notation.