∅

A

B

A∩B

A∪B

\bar { A } 

\bar { B }

A-B

B-A

A∪\bar { B }

B∪\bar { A }

\bar { A } ∩\bar { B } 

\bar { A } ∪\bar { B }

\left( A-B  \right)  ∪\left( B-A  \right) 

\left( A∩B  \right)  ∪\left(\bar { A }  ∩ \bar{B}  \right) 

S

Suceso

Prob.

Fr. Rels.

S

A

B

0

1

A-B

B-A

A∧B

-A∧-B

U = (-3, 6)
W = (7, 6)
áreaS, a, b, c, d, V, D = Polygon(W, U, 4)
B = PointIn(áreaS)
i = OrthogonalLine(B, c)
J = Intersect(i, c)
j = OrthogonalLine(B, i)
I = Intersect(j, d)
polígono4, c_1, i_1, d_2, j_1 = Polygon(B, I, D, J)
B' = PointIn(polígono4)
A = PointIn(áreaS)
V_1: (Max[x(A), x(B)], Min[y(A), y(B)])
f_2 = OrthogonalLine(A, a)
E = Intersect(f_2, c)
e = OrthogonalLine(A, b)
F = Intersect(e, d)
polígono2, a_1, f_1, d_1, e_1 = Polygon(A, F, D, E)
A' = PointIn(polígono2)
V_2: (Min[x(A'), x(B')], Max[y(A'), y(B')])
sA(x, y) = x ≥ x(A) ∧ y ≤ y(A) ∧ x ≤ x(A') ∧ y ≥ y(A')
sB(x, y) = x ≥ x(B) ∧ y ≤ y(B) ∧ x ≤ x(B') ∧ y ≥ y(B')
sAsB(x, y) = sA(x, y) ∧ sB(x, y)
listaAB1 = RemoveUndefined({Vertex[sAsB]})
listaAB2 = RemoveUndefined(Sequence[If[sAsB(Element[listaAB1, k]), Element[listaAB1, k], NaN], k, 1, Length[listaAB1]])
áreaAB1 = ConvexHull(listaAB2)
listaAB3: {Point[áreaAB1, 0], Point[áreaAB1, 0.25], Point[áreaAB1, 0.5], Point[áreaAB1, 0.75]}
áreaAB = Max(((x(V_2) - x(V_1)) * (y(V_1) - y(V_2))), 0)
B5: áreaAB / áreaS
G: (x(A), y(A'))
H: (x(A'), y(A))
áreaA, a_2, g, b_1, h = Polygon(A, G, A', H)
disjuntos: x(A') < x(B) ∨ x(B') < x(A) ∨ y(A') > y(B) ∨ y(B') > y(A)
K: (x(B'), y(B))
C: (x(B), y(B'))
áreaB, b_2, k, b', c_2 = Polygon(B, K, B', C)
BenA: x(A) < x(B) ∧ x(A') > x(B') ∧ y(A) > y(B) ∧ y(A') < y(B')
AenB: x(A) > x(B) ∧ x(A') < x(B') ∧ y(A) < y(B) ∧ y(A') > y(B')
n = 12 (slider from 1 to 16, step -1)
B3: áreaA / áreaS
B4: áreaB / áreaS
B6: B3 + B4 - B5
B7: 1 - B3
B8: 1 - B4
B9: B3 - B5
B10: B4 - B5
B11: 1 - B10
B12: 1 - B9
B13: 1 - B6
B15: B6 - B5
B16: 1 - B15
D1 = 0
D5 = 0
D2 = 0
D3 = 0
D4 = 0
C2 = 0
C3 = 0
C4 = 0
C5 = 0
C6 = 0
C7 = 0
C8 = 0
C9 = 0
C10 = 0
C11 = 0
B2 = 0
C12 = 0
C13 = 0
C14 = 0
C15 = 0
C16 = 0
B14: 1 - B5
C17 = 0
B17 = 1
dale = -0.87 (slider from -5 to 5, step 0.01)
texto1: "" + D5 + " simulaciones"
sS(x, y) = x > x(U) ∧ y < y(U) ∧ x < x(D) ∧ y > y(D)
nA(x, y) = (x ≤ x(A) ∨ y ≥ y(A) ∨ x ≥ x(A') ∨ y ≤ y(A')) ∧ sS(x, y)
nB(x, y) = (x ≤ x(B) ∨ y ≥ y(B) ∨ x ≥ x(B') ∨ y ≤ y(B')) ∧ sS(x, y)
sAnB(x, y) = sA(x, y) ∧ nB(x, y)
sBnA(x, y) = sB(x, y) ∧ nA(x, y)
nAnB(x, y) = nA(x, y) ∧ nB(x, y)
sE(x, y) = sAnB(x, y) ∨ sBnA(x, y)
nE(x, y) = sAsB(x, y) ∨ nAnB(x, y)
Pale = (1.3822371829514886, 3.4974557878858072)
Pale': Pale
dif = 0.464
vertical = 0.57
L = (8.504, 5.726)
hor1 = 2.7
hor2: hor1 + 1
columna1 = Sequence(L - (0, (k * vertical)), k, 0, 17)
columna2 = Sequence(L + (hor1, ((-k) * vertical)), k, 0, 17)
columna3 = Sequence(L + (hor2, ((-k) * vertical)), k, 0, 17)
red: {Sequence[Segment[U + (i, 0), V + (i, 0)], i, 1, 9], Sequence[Segment[D + (0, i), V + (0, i)], i, 1, 9]}
hor3: hor2 + 1.2
b10: "" + (LaTeX[B4 - B5]) + ""
b11: "" + (LaTeX[1 - B10]) + ""
b12: "" + (LaTeX[1 - B9]) + ""
b13: "" + (LaTeX[1 - B6]) + ""
b14: "" + (LaTeX[1 - B5]) + ""
b15: "" + (LaTeX[B6 - B5]) + ""
b16: "" + (LaTeX[1 - B15]) + ""
b3: "" + (LaTeX[áreaA / áreaS]) + ""
b4: "" + (LaTeX[áreaB / áreaS]) + ""
b6: "" + (LaTeX[B3 + B4 - B5]) + ""
b7: "" + (LaTeX[1 - B3]) + ""
b8: "" + (LaTeX[1 - B4]) + ""
b9: "" + (LaTeX[B3 - B5]) + ""
c10: "" + (LaTeX[C10]) + ""
c11: "" + (LaTeX[C11]) + ""
c12: "" + (LaTeX[C12]) + ""
c13: "" + (LaTeX[C13]) + ""
c14: "" + (LaTeX[C14]) + ""
c15: "" + (LaTeX[C15]) + ""
c16: "" + (LaTeX[C16]) + ""
c17: "" + (LaTeX[C17]) + ""
c2: "" + (LaTeX[C2]) + ""
c3: "" + (LaTeX[C3]) + ""
c4: "" + (LaTeX[C4]) + ""
c5: "" + (LaTeX[C5]) + ""
c6: "" + (LaTeX[C6]) + ""
c7: "" + (LaTeX[C7]) + ""
c8: "" + (LaTeX[C8]) + ""
c9: "" + (LaTeX[C9]) + ""
inc = 0.1
elegido = Polygon({L + ((-inc), ((n - 17) * vertical) + inc), L + (hor1 - inc, ((n - 17) * vertical) + inc), L + (hor1 - inc, ((n - 18) * vertical) + inc), L + ((-inc), ((n - 18) * vertical) + inc)})
tabla: {Sequence[Segment[L + ((-inc), ((-k) * vertical) + inc), L + (hor3 - inc, ((-k) * vertical) + inc)], k, 0, 17], Segment[L + ((-inc), inc), L + ((-inc), (-17 * vertical) + inc)], Segment[L + (hor1 - inc, inc), L + (hor1 - inc, (-17 * vertical) + inc)], Segment[L + (hor2 - inc, inc), L + (hor2 - inc, (-17 * vertical) + inc)], Segment[L + (hor3 - inc, inc), L + (hor3 - inc, (-17 * vertical) + inc)]}
E2 = 0
F2 = 0
G2 = 0
H2: 0
E3 = 1
F3 = 0
G3 = 1
H3 = 0
E4 = 0
F4 = 1
G4 = 1
H4 = 0
E5 = 0
F5 = 0
G5 = 1
H5 = 0
E6 = 1
F6 = 1
G6 = 1
H6 = 0
E7 = 0
F7 = 1
G7 = 0
H7 = 1
E8 = 1
F8 = 0
G8 = 0
H8 = 1
E9 = 1
F9 = 0
G9 = 0
H9 = 0
E10 = 0
F10 = 1
G10 = 0
H10 = 0
E11 = 1
F11 = 0
G11 = 1
H11 = 1
E12 = 0
F12 = 1
G12 = 1
H12 = 1
E13 = 0
F13 = 0
G13 = 0
H13 = 1
E14 = 1
F14 = 1
G14 = 0
H14 = 1
E15 = 1
F15 = 1
G15 = 0
H15 = 0
E16 = 0
F16 = 0
G16 = 1
H16 = 1
E17 = 1
F17 = 1
G17 = 1
H17 = 1
I2: 0
J2: 0
K2: 0
L2: 0
b5: "" + (LaTeX[B5]) + ""