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78- % ST ^ A ] A Y A b A Z A j A [ A q A \ A m U n+44+6 '
"
1. (A ! B)
2. (A$C) # B
#C
3. (A # B # C) ! (A" ! B' )
?84/70>-'
"
1. (A # B) ! C
2. (A$C )
!B
=
=
{0,1,2,3,4,5,6}" ! {1,2,4,6,7} {7,8,9}! {1,2,4,6,7} {7} =
=
[(A # C) " (C # A)]! B ({3}" {6,7}) ! {0,2,5,6} {6}
3. (A # B # C) ! (A" ! B")
=
=
=
{2}! {0,1,3,5,6,7,8,9} {0,1,2,3,5,6,7,8,9} =
33
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-`@a d -`Ha
?84/70>-'
Sabemos que : n(A " B) = n(A) + n(B) - n(A ! B) Se tiene :
n(A) + n(B) - n(A ! B) = 60 ......(1)
Sabemos que : n(A " B) n(A) - n(A ! B) =
n(A) - n(A ! B) Como B ! A$
=
=
24 .......... ......(2)
B - A # n(B " A) n(B) - n(B ! A) =
n(B) - n(A ! B)
20 .......... ......(3)
J*:.+-)8 '
`]a
J*:.+-)8 '
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2/*;8
F `Ya :* .0*-* '
=
-`Ha S b[
-`@a d -`Ha S Z^ d b[ S q[
34
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5a
C`@a . C`Ha
?84/70>-'
Como : A a. A " C
{a, {a, b}}; B {a, b, {c}} C A $ B {{a, b}} {{a, b}} # P(A " C) { {{a, b}} , ! }
=
=
=
=
=
, entonces
=
{ {a}, {{a, b}}, {a, {a, b} }! } P(B) { {a}, {b}, {{c }}, {a, b}, {a, {c}}, {b, {c}}, {a, b, {c}}, ! } P(A) " P(B) { {a}, ! }
b. P(A)
=
=
=
35
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SOLUCIÓN
A=25
B=33
n(A) = 25 n(B) = 33 n(C) = 40
n(A/ 0 / 12 - 3
18-a-b
b
26-b-c
7 a
c
C=40 RPTA:22 33-a-c
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n(I)
=
40
n(F)
n(A) 16 =
28
n(I " F) 12
=
n(I " A)
=
=
5
n(A " F " I!)
n(A " F " I) =
x
=
2
h
( 25
10 3
2
28-(10+2+x) x
16-(3+2+x) @ 37
I$IJ!(!("? KI !"#$%#&"?
7.
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SOLUCIONARIO Hombres
Mujeres 17 años
Mujeres que no tienen 18 años: p + 5 = 14
A 5
Mujeres que no tienen 17 años : p
10 18 años
p=9
p + q = 16
q=7
10 + ( A + B ) + 5 + 7 + 9 = 50 B q
Luego: A + B = 19
39
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