Explicación completa de los conjunto e intervalos.

1. Universidad Central del Ecuador
Facultad de Ciencias Químicas
Nivelación Matemática
Integrantes:
• Aaron Alonso Uvidia Jurado
• Yehileen Naizeth Moreira Loor
• María Gabriela Santillán Muyulema
• Giscela Jacqueline Sisalema Analuca
Grupo N° 3

2. 𝐴 = {0}
𝐵 = {𝑎, 𝑔, 𝑟, 𝑖, 𝑐, 𝑢, 𝑙, 𝑡, 𝑜}
𝐶 = {−1,0,1}
𝐷 = {2,4,6,8,10,12,14}
𝐸 = ∅
𝐹 = {2,4,6,8,10,12,14, … , 1532, … }
𝐺 = {… , −30235, … , −10, −5,0,5,10, … , 10000, … }
𝐻 = {𝑃𝑒𝑟ú, 𝑃𝑎𝑛𝑎𝑚á, 𝑃𝑎𝑟𝑎𝑔𝑢𝑎𝑦}
𝐼 = {𝐹𝑒𝑟𝑛𝑎𝑛𝑑𝑜 𝑆𝑒𝑚𝑝é𝑟𝑡𝑒𝑔𝑢𝑖 𝑂𝑛𝑡𝑎𝑛𝑒𝑑𝑎 𝑉𝑖𝑙𝑙𝑎𝑙𝑏𝑎 𝑃ℎ𝐷. }
𝐽 = {𝐷𝑒𝑛𝑛𝑖𝑠, 𝐶𝑎𝑟𝑙𝑜𝑠, 𝐽𝑎𝑣𝑖𝑒𝑟, 𝐶𝑟𝑖𝑠𝑡𝑖𝑎𝑛, 𝐸𝑙𝑣𝑖𝑎}

3. 𝐴 = {𝑥/𝑥 𝑒𝑠 𝑢𝑛𝑎 𝑣𝑜𝑐𝑎𝑙}
𝐵 = {𝑥/𝑥 ∈ ℕ 𝑦 𝑒𝑠 𝑝𝑟𝑖𝑚𝑜}
𝐶 = {𝑥/𝑥 ∈ ℕ, 𝑥 = 2𝑛 − 1}
𝐷 = {𝑥/𝑥 𝑒𝑠 𝑒𝑙 𝑎𝑏𝑒𝑐𝑒𝑑𝑎𝑟𝑖𝑜}
𝐸 = {𝑥/𝑥 ∈ ℕ, 𝑥 = 𝑛2 ∧ 𝑥 ≠ 1}
𝐹 = {𝑥/𝑥 ∈ ℕ, 1 ≤ 𝑥 ≤ 9}
𝐺 = {𝑥/𝑥 ∈ ℤ, 0 ≤ 𝑥 ≤ 9}
𝐻 = {𝑥/𝑥 ∈ ℤ, 𝑥 = 2}
𝐼 = {𝑥/𝑥 𝑒𝑠 𝑙𝑎 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑑𝑒 𝑆𝑎𝑛𝑡𝑜 𝐷𝑜𝑚𝑖𝑛𝑔𝑜 𝑑𝑒 𝑙𝑜𝑠 𝑇𝑠á𝑐ℎ𝑖𝑙𝑎𝑠}
𝐽 = {𝑥/𝑥 ∈ ℝ, 𝑥 = −1}

4. 𝐴 = {𝑥/𝑥 < 3}
𝐵 = {𝑥/𝑥 ≥ 2}
𝐶 = {𝑥/𝑥 ≥ 1}
𝐷 = {𝑥/𝑥 > −1}
3
2
1
-1
𝐴 =] − ∞; 3[
𝐵 = [2; +∞[
𝐶 = [1; +∞[
𝐷 =] − 1; +∞[

5. 𝐵
𝐴
𝐴 ∪ 𝐵
-4 -3 -2 -1 0 1 2 3 4
𝐴 ∩ 𝐵
𝐴 ∪ 𝐵 = [−3; 2] 𝐴 ∩ 𝐵=[-1;1[

6. a) {𝑥/𝑥 > −1} ∩ {𝑥/−3 < 𝑥 < 2}
b) {𝑥/𝑥 < 2} ∪ {𝑥/𝑥 ≥ 2}
c) {𝑥/−3 < 𝑥 ≤ 1} ∩ {𝑥/𝑥 > 2}
d) {𝑥/−2 < 𝑥 ≤ 3} ∪ {𝑥/𝑥 < 1}
e) {𝑥/−3 ≤ 𝑥 ≤ 0} ∩ {𝑥/−2 < 𝑥 < 3}
-4 -3 -2 -1 0 1 2 3 4
-4 -3 -2 -1 0 1 2 3 4
-4 -3 -2 -1 0 1 2 3 4
-4 -3 -2 -1 0 1 2 3 4
-4 -3 -2 -1 0 1 2 3 4
A B
A
B
A
B
A
B
A
B
A
B 𝐴 ∪ 𝐵
𝐴 ∩ 𝐵
𝐴 ∪ 𝐵
𝐴 ∩ 𝐵
𝐴 ∪ 𝐵 = ℝ
𝐴 ∩ 𝐵 =] − 2; 0]
𝐴 ∪ 𝐵 =] − ∞; 3]
𝐴 ∩ 𝐵 = ∅
𝐴 ∩ 𝐵 =] − 1; 2[

7. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
𝐴 ∪ 𝐵 = [−4; 6[
𝐴 ∩ 𝐵 =] − 1; 2[
𝐴 ∪ 𝐶 =] − ∞; 2[
A
B
C
A
B
A
𝐴 ∪ 𝐵
𝐴 ∩ 𝐵
𝐴 ∪ 𝐶

8. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
𝐴 ∩ 𝐶 = [−4; 1]
𝐵 ∪ 𝐶 =] − ∞; 6[
𝐵 ∩ 𝐶 =] − 1; 1]
A
B
C
C
C
B
𝐴 ∩ 𝐶
𝐵 ∪ 𝐶
𝐵 ∩ 𝐶

9. 𝐴𝑥𝐵 = { −2,1 −2,2 −2,3 0,1 0,2 0,3
3,1 3,2 3,3 7,1 7,2 7,3 }
𝐵𝑥𝐴 = { 1, −2 1,0 1,3 1,7 2, −2 2,0
2,3 2,7 3, −2 3,0 3,3 3,7 }
-2
0
3
7
1
2
3
1
2
3
-2
0
3
7
A
B
B
A
∙
∙
∙ ∙
∙
∙ ∙
∙
∙
∙∙∙
∙
∙
∙
∙
∙
∙
∙
∙
∙
∙
∙
∙
𝐴𝑥𝐵
A B
𝐵𝑥A
B A

10. 𝑇𝑥𝑆 = { 1,1 1,2 2,1 2,2 3,1
3,2 4,1 4,2 5,1 5,2 }
𝑆𝑥𝑇 = { 1,1 1,2 1,3 1,4 1,5
2,1 2,2 2,3 2,4 2,5 }
1
2
3
4
5
1
2
1
2
1
2
3
4
5
T
S
S
T
∙
∙∙
∙∙
∙∙∙
∙
∙
∙
∙
∙
∙
∙∙
∙
∙
∙
∙
𝑇𝑥𝑆
T S
𝑆𝑥T
S T

11. 𝐴𝑥𝐵 = { −1, −2 −1,0 1, −2 1,0 … }
𝐵𝑥𝐴 = { −2, −1 −2,1 0, −1 0,1 … }
-1
1
.
.
-2
0
.
.
-2
0
.
.
-1
1
.
.
𝐴 = {−1,1, … . }
𝐵 = {−2,0, … . }
A
B
B
A
𝐴𝑥𝐵
A B
𝐴𝑥𝐵
A B

12. 𝐾𝑥𝐽 = { −3,2 −3,5 0,2 0,5 … }
𝐽𝑥𝐾 = { 2, −3 2,0 5, −3 5,0 … }
-3
0
.
.
2
5
.
.
2
5
.
.
-3
0
.
.
𝐾 = {−3,0, … }
𝐽 = {2,5, … . }
K
J
J
K
𝐾𝑥𝐽
K J
𝐽𝑥𝐾
J K

13. ℝ𝑥𝐴 = {… −5,2 −5,4 5,2 5,4 … }
𝐴𝑥ℝ = {… 2, −5 2,5 4, −5 4,5 … }
.
.
-5
5
.
.
2
.
.
4
2
.
.
4
.
.
-5
5
.
.
ℝ = {… , −5,5, … . }
𝐴 = {2, … , 4}
ℝ
A
A
ℝ
ℝ𝑥A
ℝ A
𝐴𝑥ℝ ℝ
A