Intervalo o entorno:

Intervalo:

Segundo intervalo

Operación:

lista3: {"(a, b)", "[a, b]", "[a, b)", "(a, b]", "E(a, r)", "E[a, r]", "E*(a, r)"}
op1 = SelectedIndex(lista3)
A = Point(a)
B = Point(Ray[A, A + (1, 0)])
conjunto1ca: "\left\{x∈ℝ/" + (LaTeX[x(A)]) + " ≤ x < " + (LaTeX[x(B)]) + "\right\} "
conjunto1cc: "\left\{x∈ℝ/" + (LaTeX[x(A)]) + " ≤ x ≤ " + (LaTeX[x(B)]) + "\right\} "
conjunto1ac: "\left\{x∈ℝ/" + (LaTeX[x(A)]) + " < x ≤ " + (LaTeX[x(B)]) + "\right\} "
conjunto1aa: "\left\{x∈ℝ/" + (LaTeX[x(A)]) + " < x < " + (LaTeX[x(B)]) + "\right\} "
E = Point(xAxis)
F = Point(Ray[E, E + (0, 1)])
r = Segment(E, F)
conjunto1e3: "\left\{x∈ℝ/" + (LaTeX[x(E) - r]) + " < x < " + (LaTeX[x(E)]) + ((" ∨ " * LaTeX[x(E)])) + " < x < " + (LaTeX[x(E) + r]) + "\right\} "
conjunto1e2: "\left\{x∈ℝ/" + (LaTeX[x(E) - r]) + " ≤ x ≤ " + (LaTeX[x(E) + r]) + "\right\} "
conjunto1e1: "\left\{x∈ℝ/" + (LaTeX[x(E) - r]) + " < x < " + (LaTeX[x(E) + r]) + "\right\} "
C = Point(b)
D = Point(Ray[C, C + (1, 0)])
ABcc(x) = x(A) ≤ x ≤ x(B)
CDcc(x) = x(C) ≤ x ≤ x(D)
ABca(x) = x(A) ≤ x  <  x(B)
ABac(x) = x(A)  <  x ≤ x(B)
ABaa(x) = x(A)  <  x  <  x(B)
CDca(x) = x(C) ≤ x  <  x(D)
CDaa(x) = x(C)  <  x  <  x(D)
CDac(x) = x(C)  <  x ≤ x(D)
lista4: {"(c, d)", "[c, d]", "[c, d)", "(c, d]"}
segundointervalo = false
AB = If(op1 ≟ 1, ABaa, op1 ≟ 2, ABcc, op1 ≟ 3, ABca, op1 ≟ 4, ABac)
op2 = SelectedIndex(lista4)
CD = If(op2 ≟ 1, CDaa, op2 ≟ 2, CDcc, op2 ≟ 3, CDca, op2 ≟ 4, CDac)
G: E + (abs(F - E), 0)
cc = Circle(E, G)
ca = Circle(E, F)
caso = If(x(B)  <  x(C), 1, x(B) ≟ x(C), 2, (x(A)  <  x(C)) ∧ (x(C)  <  x(B)) ∧ (x(B)  <  x(D)), 3, (x(A)  <  x(C)) ∧ x(B) ≟ x(D), 4, (x(A)  <  x(C)) ∧ (x(D)  <  x(B)), 5, x(A) ≟ x(C) ∧ (x(B)  <  x(D)), 6, x(A) ≟ x(C) ∧ x(B) ≟ x(D), 7, x(A) ≟ x(C) ∧ (x(D)  <  x(B)), 8, (x(C)  <  x(A)) ∧ (x(B)  <  x(D)), 9, (x(C)  <  x(A)) ∧ x(B) ≟ x(D), 10, (x(C)  <  x(A)) ∧ (x(A)  <  x(D)) ∧ (x(D)  <  x(B)), 11, x(D) ≟ x(A), 12, x(D)  <  x(A), 13)
abA: op1 ≟ 1 ∨ op1 ≟ 4
abB: op1 ≟ 1 ∨ op1 ≟ 3
abC: op2 ≟ 1 ∨ op2 ≟ 4
abD: op2 ≟ 1 ∨ op2 ≟ 3
nomostrar: caso ≟ 1 ∨ caso ≟ 2 ∧ (abB ∨ abC) ∨ caso ≟ 12 ∧ (abA ∨ abD) ∨ caso ≟ 13
i02(x) = x(B) ≤ x ≤ x(B)
lista1: {Polygon[A, B, (x(B), -1), (x(A), -1)]}
lista2: {Polygon[C, D, (x(D), 1), (x(C), 1)]}
minInt = If(caso  <  9, x(C), x(A))
maxInt = If(caso ≟ 5 ∨ caso ≟ 8 ∨ caso ≟ 11, x(D), x(B))
i03 = If(abC ∧ abB, minInt  <  x  <  maxInt, abC, minInt  <  x ≤ maxInt, abB, minInt ≤ x  <  maxInt, minInt ≤ x ≤ maxInt)
i05: CD
i04 = If(abC ∧ (abB ∨ abD), minInt  <  x  <  maxInt, abC ∧ (¬abB) ∧ (¬abD), minInt  <  x ≤ maxInt, (¬abC) ∧ (abB ∨ abD), minInt ≤ x  <  maxInt, minInt ≤ x ≤ maxInt)
i06 = If(abD ∧ (abA ∨ abC), minInt  <  x  <  maxInt, (abA ∨ abC) ∧ (¬abB), minInt  <  x ≤ maxInt, (¬abC) ∧ (¬abA) ∧ abB, minInt ≤ x  <  maxInt, minInt ≤ x ≤ maxInt)
i07 = If((abB ∨ abD) ∧ (abA ∨ abC), minInt  <  x  <  maxInt, (abA ∨ abC) ∧ (¬abB) ∧ (¬abD), minInt  <  x ≤ maxInt, (¬abC) ∧ (¬abA) ∧ (abB ∨ abD), minInt ≤ x  <  maxInt, minInt ≤ x ≤ maxInt)
i08 = If(abD ∧ (abA ∨ abC), minInt  <  x  <  maxInt, (abC ∨ abA) ∧ (¬abD), minInt  <  x ≤ maxInt, (¬abC) ∧ (¬abA) ∧ abD, minInt ≤ x  <  maxInt, minInt ≤ x ≤ maxInt)
i09: AB
i10 = If(abA ∧ (abB ∨ abD), minInt  <  x  <  maxInt, abA ∧ (¬abB) ∧ (¬abD), minInt  <  x ≤ maxInt, (¬abA) ∧ (abD ∨ abB), minInt ≤ x  <  maxInt, minInt ≤ x ≤ maxInt)
Ra(x) = (2 * x(E)) - x(G)  <  x  <  x(G)
Raa(x) = (2 * x(E)) - x(G)  <  x  <  x(E) ∨ x(E)  <  x  <  x(G)
Rc(x) = (2 * x(E)) - x(G) ≤ x ≤ x(G)
i11 = If(abA ∧ abD, minInt  <  x  <  maxInt, abA, minInt  <  x ≤ maxInt, abD, minInt ≤ x  <  maxInt, minInt ≤ x ≤ maxInt)
i12(x) = x(A) ≤ x ≤ x(A)
lista5: {"Sin operación", "Unión", "Intersección"}
op3 = SelectedIndex(lista5)
sa02: "\left\{ " + (LaTeX[minInt]) + " \right\} "
sa03: If[abC ∧ abB ∨ abC ∧ (¬abB), "(", "["] + ((minInt * ", "))
sa04: If[abC ∧ (abB ∨ abD) ∨ abC ∧ (¬abB) ∧ (¬abD), "(", "["] + ((minInt * ", "))
sa05: If[op2 ≟ 1 ∨ op2 ≟ 4, "(", "["] + ((minInt * ", "))
sa06: If[abD ∧ (abA ∨ abC) ∨ (abA ∨ abC) ∧ (¬abB), "(", "["] + ((minInt * ", "))
sa07: If[(abB ∨ abD) ∧ (abA ∨ abC) ∨ (abA ∨ abC) ∧ (¬abB) ∧ (¬abD), "(", "["] + ((minInt * ", "))
sa08: If[abD ∧ (abA ∨ abC) ∨ (abC ∨ abA) ∧ (¬abD), "(", "["] + ((minInt * ", "))
sa09: If[op1 ≟ 1 ∨ op1 ≟ 4, "(", "["] + ((minInt * ", "))
sa10: If[abA ∧ (abB ∨ abD) ∨ abA ∧ (¬abB) ∧ (¬abD), "(", "["] + ((minInt * ", "))
sa11: If[abA ∧ abD ∨ abA ∧ (¬abD), "(", "["] + ((minInt * ", "))
sa12: "\left\{ " + (LaTeX[minInt]) + " \right\} "
sb03: (maxInt * If[abC ∧ abB ∨ (¬abC) ∧ abB, ")", "]"])
sb04: (maxInt * If[abC ∧ (abB ∨ abD) ∨ (¬abC) ∧ (abB ∨ abD), ")", "]"])
sb05: (maxInt * If[op2 ≟ 1 ∨ op2 ≟ 3, ")", "]"])
sb06: (maxInt * If[abD ∧ (abA ∨ abC) ∨ (¬abC) ∧ (¬abA) ∧ abB, ")", "]"])
sb07: (maxInt * If[(abB ∨ abD) ∧ (abA ∨ abC) ∨ (¬abC) ∧ (¬abA) ∧ (abB ∨ abD), ")", "]"])
sb08: (maxInt * If[abD ∧ (abA ∨ abC) ∨ (¬abC) ∧ (¬abA) ∧ abD, ")", "]"])
sb09: (maxInt * If[op1 ≟ 1 ∨ op1 ≟ 3, ")", "]"])
sb10: (maxInt * If[abA ∧ (abB ∨ abD) ∨ (¬abA) ∧ (abD ∨ abB), ")", "]"])
sb11: (maxInt * If[abA ∧ abD ∨ (¬abA) ∧ abD, ")", "]"])
sa = Element({"ϕ", If[(op1 ≟ 2 ∨ op1 ≟ 4) ∧ (op2 ≟ 2 ∨ op2 ≟ 3), sa02, "ϕ"], sa03, sa04, sa05, sa06, sa07, sa08, sa09, sa10, sa11, If[(op1 ≟ 2 ∨ op1 ≟ 3) ∧ (op2 ≟ 2 ∨ op2 ≟ 4), sa12, "ϕ"], "ϕ"}, caso)
sb = Element({"", sb02, sb03, sb04, sb05, sb06, sb07, sb08, sb09, sb10, sb11, sb12, ""}, caso)
intervalo1 = If(x(A) ≟ x(B) ∧ (op1 ≠ 2), "ϕ", x(A) ≟ x(B), "\left\{ " + (LaTeX[x(A)]) + " \right\} ", Element[{(((("(" * x(A)) * ", ") * x(B)) * ")"), (((("[" * x(A)) * ", ") * x(B)) * "]"), (((("[" * x(A)) * ", ") * x(B)) * ")"), (((("(" * x(A)) * ", ") * x(B)) * "]"), (((("E(" * x(E)) * ", ") * r) * ")"), (((("E[" * x(E)) * ", ") * r) * "]"), (((("E^{*}(" * x(E)) * ", ") * r) * ")")}, op1])
intervalo2 = If(x(C) ≟ x(D) ∧ (op2 ≠ 2), "ϕ", x(C) ≟ x(D), "\left\{ " + (LaTeX[x(C)]) + " \right\} ", Element[{(((("(" * x(C)) * ", ") * x(D)) * ")"), (((("[" * x(C)) * ", ") * x(D)) * "]"), (((("[" * x(C)) * ", ") * x(D)) * ")"), (((("(" * x(C)) * ", ") * x(D)) * "]")}, op2])
lista1': {Polygon[A, B, (x(B), -1), (x(A), -1)]}
lista2': {Polygon[C, D, (x(D), 1), (x(C), 1)]}
clo1aa: "\left\{x∈ℝ/" + (LaTeX[x(A)]) + " < x < " + (LaTeX[x(B)]) + "\right\} "
conjunto2aa: "\left\{x∈ℝ/" + (LaTeX[x(C)]) + " < x < " + (LaTeX[x(D)]) + "\right\} "
conjunto2ac: "\left\{x∈ℝ/" + (LaTeX[x(C)]) + " < x ≤ " + (LaTeX[x(D)]) + "\right\} "
conjunto2ca: "\left\{x∈ℝ/" + (LaTeX[x(C)]) + " ≤ x < " + (LaTeX[x(D)]) + "\right\} "
conjunto1 = Element({conjunto1aa, conjunto1cc, conjunto1ca, conjunto1ac, conjunto1e1, conjunto1e2, conjunto1e3}, op1)
conjunto2cc: "\left\{x∈ℝ/" + (LaTeX[x(C)]) + " ≤ x ≤ " + (LaTeX[x(D)]) + "\right\} "
texto1: "" + (LaTeX[intervalo1]) + "=" + (LaTeX[conjunto1]) + ""
conjunto2 = Element({conjunto2aa, conjunto2cc, conjunto2ca, conjunto2ac}, op2)
texto2: "" + (LaTeX[intervalo2]) + "=" + (LaTeX[conjunto2]) + ""
max = If((caso  <  4) ∨ caso ≟ 6 ∨ caso ≟ 9, x(D), x(B))
min = If(caso  <  9, x(A), x(C))
sc02: If[abA, "(", "["] + ((min * ", "))
sc03: If[abA, "(", "["] + ((min * ", "))
sc04: If[abA, "(", "["] + ((min * ", "))
sc05: If[abA, "(", "["] + ((min * ", "))
sc06: If[abA ∧ abC, "(", "["] + ((min * ", "))
sc07: If[abA ∧ abC, "(", "["] + ((min * ", "))
sc08: If[abA ∧ abC, "(", "["] + ((min * ", "))
sc09: If[abC, "(", "["] + ((min * ", "))
sc10: If[abC, "(", "["] + ((min * ", "))
sc11: If[abC, "(", "["] + ((min * ", "))
sc12: If[abC, "(", "["] + ((min * ", "))
sd02: (max * If[abD, ")", "]"])
sd03: (max * If[abD, ")", "]"])
sd04: (max * If[abD ∧ abB, ")", "]"])
sd05: (max * If[abB, ")", "]"])
sd06: (max * If[abD, ")", "]"])
sd07: (max * If[abD ∧ abB, ")", "]"])
sd08: (max * If[abB, ")", "]"])
sd09: (max * If[abD, ")", "]"])
sd10: (max * If[abD ∧ abB, ")", "]"])
sd11: (max * If[abB, ")", "]"])
sd12: (max * If[abB, ")", "]"])
scd = Element({((intervalo1 * "∪") * intervalo2), If[abB ∧ abC, ((intervalo1 * "∪") * intervalo2), (sc02 * sd02)], (sc03 * sd03), (sc04 * sd04), (sc05 * sd05), (sc06 * sd06), (sc07 * sd07), (sc08 * sd08), (sc09 * sd09), (sc10 * sd10), (sc11 * sd11), If[abA ∧ abD, ((intervalo2 * "∪") * intervalo1), (sc12 * sd12)], ((intervalo2 * "∪") * intervalo1)}, caso)
u01(x) = AB(x) ∨ CD(x)
u13(x) = CD(x) ∨ AB(x)
u04 = If(abA ∧ abD ∧ abB, x(A)  <  x  <  x(D), abA, x(A)  <  x ≤ x(D), abD ∧ abB, x(A) ≤ x  <  x(D), x(A) ≤ x ≤ x(D))
u02 = If(abB ∧ abC, AB(x) ∨ CD(x), abA ∧ abD, x(A)  <  x  <  x(D), abA, x(A)  <  x ≤ x(D), abD, x(A) ≤ x  <  x(D), x(A) ≤ x ≤ x(D))
u03 = If(abA ∧ abD, x(A)  <  x  <  x(D), abA, x(A)  <  x ≤ x(D), abD, x(A) ≤ x  <  x(D), x(A) ≤ x ≤ x(D))
u12 = If(abA ∧ abD, CD(x) ∨ AB(x), abC ∧ abB, x(C)  <  x  <  x(B), abC, x(C)  <  x ≤ x(B), abB, x(C) ≤ x  <  x(B), x(C) ≤ x ≤ x(B))
u05 = If(abA ∧ abB, x(A)  <  x  <  x(B), abA, x(A)  <  x ≤ x(B), abB, x(A) ≤ x  <  x(B), x(A) ≤ x ≤ x(B))
u06 = If(abA ∧ abC ∧ abD, x(A)  <  x  <  x(D), abA ∧ abC, x(A)  <  x ≤ x(D), abD, x(A) ≤ x  <  x(D), x(A) ≤ x ≤ x(D))
u07 = If(abA ∧ abB ∧ abC ∧ abD, x(A)  <  x  <  x(D), abA ∧ abC, x(A)  <  x ≤ x(D), abB ∧ abD, x(A) ≤ x  <  x(D), x(A) ≤ x ≤ x(D))
u08 = If(abA ∧ abC ∧ abB, x(A)  <  x  <  x(B), abA ∧ abC, x(A)  <  x ≤ x(B), abB, x(A) ≤ x  <  x(B), x(A) ≤ x ≤ x(B))
u09 = If(abC ∧ abD, x(C)  <  x  <  x(D), abC, x(C)  <  x ≤ x(D), abD, x(C) ≤ x  <  x(D), x(C) ≤ x ≤ x(D))
u10 = If(abC ∧ abD ∧ abB, x(C)  <  x  <  x(D), abC, x(C)  <  x ≤ x(D), abD ∧ abB, x(C) ≤ x  <  x(D), x(C) ≤ x ≤ x(D))
u11 = If(abC ∧ abB, x(C)  <  x  <  x(B), abC, x(C)  <  x ≤ x(B), abB, x(C) ≤ x  <  x(B), x(C) ≤ x ≤ x(B))
i01: 0 < x < 0
i13: 0 < x < 0
lista6: {i01, i02, i03, i04, i05, i06, i07, i08, i09, i10, i11, i12, i13}
intersección = Element(lista6, caso)
lista7: {u01, u02, u03, u04, u05, u06, u07, u08, u09, u10, u11, u12, u13}
unión = Element(lista7, caso)
intervalo3: "Resultado:  " + (LaTeX[(sa * sb)]) + ""
intervalo4_1: "Resultado:  " + (LaTeX[scd]) + ""
lista1b, a_1, b_1, c, d = Polygon(A, B, (x(B), -1), (x(A), -1))
lista1b', a_2, b_2, e, f = Polygon(A, B, (x(B), -1), (x(A), -1))
lista2b, c_1, d_1, g, h = Polygon(C, D, (x(D), 1), (x(C), 1))
lista2b', c_2, d_2, i, j = Polygon(C, D, (x(D), 1), (x(C), 1))