Write the following set in Builder Set Notation. a) {0, 3, 6, 9, 12 { b) {.3,.2,.1, 0, 1, 2, 3{ c) { 10,15,20,25,30,35}
1) Write the following set in Builder Set Notation.
a) {0, 3, 6, 9, 12 {
b) {.3,.2,.1, 0, 1, 2, 3{
c) { 10,15,20,25,30,35}
2) Determine whether each of these statements is true or false:
a) { 1} ∈ { 1,2,3,4,5}
b) x ∈ {x}
c) {x} ⊆ {x}
d) {x} ∈ {x}
e) {x} ∈ {{x}}
f) ф ⊆ {x}
3) Determine whether each of these sets is a power set of any set, where a and b are distinct
elements .
a) ∅
b) {∅, {a}}
c) {∅, {a}, {∅, a}}
d) {∅, {a}, {b}, {a, b}}
4) Briefly justify why the following statements are true or false.
a) If A is the set of letters in the word ‘flabbergasted,’ then |A| = 13.
b) For the set A in the previous part, we have a ∈ A or z ∈ A.
c) If B = {n | n ∈ Z, 10 ≤ n ≤ 20} then |B| = 10.
d) For the set B in the previous part we have 11 ∈ B and √200 ∈ B.
e) If L is the set of letters in "banana", then a ∈ L.
5) Let A = {a, b, c}, B = {x, y}, and C = {0, 1}, Find:
a) A × B × C
b) C × B
c) B × B × B
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