Math 151 HW 1 Solutions
Problems
1.
With replacing: S=
{
(red, red),(red,green),(red,blue),(green,red),(green, green), (green, blue),(blue,
red),(blue,green),(blue,blue)
}
Without replacing: S=
{
(red,green),(red,blue),(green,red), (green, blue),(blue, red),(blue,green)
}
2.
S
=
{
6
, x
6
, xx
6
, xxx
6
, ...
} ∪ {
no 6 appears
}
Here
xxx
6 means that 6 appears on 4th trial.
x
is
anything other than 6.
x
s on diﬀerent positions may represent diﬀerent numbers.
Using this notation,
E
n
=
{
n

1 times x followed by 6
}
And (
∪
E
n
)
C
) =
{
no 6 appears
}
3.
E
∩
F
=
{
(1,2), (1,4), (1,6), (2,1), (4,1), (6,1)
}
E
∪
F
=
{
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,3), (2,5), (3,1), (3,2), (3,4), (3,6), (4,1), (4,3),
(4,5), (5,1), (5,2), (5,4), (5,6), (6,1), (6,3), (6,5)
}
F
∩
G
=
{
(1,4), (4,1)
}
E
∩
F
C
=
{
(2,3), (2,5), (3,2), (3,4), (3,6), (4,3), (4,5), (5,2), (5,4), (5,6), (6,3), (6,5)
}
E
∩
F
∩
G
=
{
(1,4), (4,1)
}
4.
(a) This is similar to the solution of problem 2 above. If 1 comes up at positions 3