sets exercises
week 1 Sets
12 the set of all
integers that are divisible by 7 or 11.
Ex :
* X or 13
[x : (x
mody
=
0) or (xmod11 =
0)]
D all the real roots of the polynomial XS-GX2 + 11X-6
Ex + IR :
X -
0x2 + 1x
-
0 =
03
cG(X , y)
:
(3x -
y = 0)1(x +
2y
=
7))
2u : =
21 ,
2
, ..., 303
multiples o2
f =
M2
multiples of 3 =
M3
multiples of 5
=
M5
a M2 / M5 =
M2 + M5
b M21 M3 1 M5
c (M2' + M3) e (M2'1 M5Y
a9303 =
2 * 3x5
M2 1 M3 1 M5
.
3 universe of IR numbers
·
A : =
(x :
0 <
x =
2)
and
B : =
Ex : 1 =
xa3]
-
AUB =
Ex : 0 < x
=
33
-
ArB =
EX : 1 = X = 2}
-
A(B =
Gx : 0 x 13
-
B1A =
GX :
c <
X
+
3)
,4a(A)(BUC))) and A ' l(BUC)
Al(BUC)
·
A A
B B
I
&
7
2 2
↓
(A)(BUC))'
]
A A
B B
-
not the
2 2
same !'
Al
A'n(Buc)
A A
B
. 2 2
2
BUC
D(A)(BMC)) and (A'U (BMC)
(A)(BUC))'
A
B
-
Stre
2
j
A u(Brc)
A A
B B
2 2
A
B
2
BMC
,C(AUB))C and (AIC) U (BIC)
AUB
A A
B B
%
2 2
Jare
A
B
2
C
A A
B B
↳
2 2
A
B
2
BIC
d A v (BAC) and (AUB) 1 (AUC)
BAC
AUB
A A
B B A
B
p I
2 2
2
NOT THE SAME
&
A
B
#
A A
B B
2
2 2
A
AUC
52 #A =
7
# B =
d 122-B
22
# c 9
=
4
# (A nB) =
# (Anc) = # (BC) =
3 2
4
# (AUBUc) =
1
# u =
20
, # (tubuc) =
1 + 2 + 2 + 2 + 2 + 3 + 4
=
16
#(A ' nB'r2) =
20 -
16
=
4
Al B' Cl
A A A
B B B
2 2 2
↳ in Binc
A
B
2
# (AUB) =
4 + 4
= 8
AUB (AUB)
A A
B B
>
-
2 2
6
⑰
100 8
x
108
goo
* (B) * /39
15 45701590265585
585
457115
# U =
1000 # (D + =) =
#DrB)UsDrA100-15
# D =
100 # (D1B) =
70
# D'
goo
=
AID
2653355
#
go
=
# B10 =
# (AUB) (D =
1000 -
505 -
100
315
=
4. (AID) (BID) =
10
-
-
week 1 Sets
12 the set of all
integers that are divisible by 7 or 11.
Ex :
* X or 13
[x : (x
mody
=
0) or (xmod11 =
0)]
D all the real roots of the polynomial XS-GX2 + 11X-6
Ex + IR :
X -
0x2 + 1x
-
0 =
03
cG(X , y)
:
(3x -
y = 0)1(x +
2y
=
7))
2u : =
21 ,
2
, ..., 303
multiples o2
f =
M2
multiples of 3 =
M3
multiples of 5
=
M5
a M2 / M5 =
M2 + M5
b M21 M3 1 M5
c (M2' + M3) e (M2'1 M5Y
a9303 =
2 * 3x5
M2 1 M3 1 M5
.
3 universe of IR numbers
·
A : =
(x :
0 <
x =
2)
and
B : =
Ex : 1 =
xa3]
-
AUB =
Ex : 0 < x
=
33
-
ArB =
EX : 1 = X = 2}
-
A(B =
Gx : 0 x 13
-
B1A =
GX :
c <
X
+
3)
,4a(A)(BUC))) and A ' l(BUC)
Al(BUC)
·
A A
B B
I
&
7
2 2
↓
(A)(BUC))'
]
A A
B B
-
not the
2 2
same !'
Al
A'n(Buc)
A A
B
. 2 2
2
BUC
D(A)(BMC)) and (A'U (BMC)
(A)(BUC))'
A
B
-
Stre
2
j
A u(Brc)
A A
B B
2 2
A
B
2
BMC
,C(AUB))C and (AIC) U (BIC)
AUB
A A
B B
%
2 2
Jare
A
B
2
C
A A
B B
↳
2 2
A
B
2
BIC
d A v (BAC) and (AUB) 1 (AUC)
BAC
AUB
A A
B B A
B
p I
2 2
2
NOT THE SAME
&
A
B
#
A A
B B
2
2 2
A
AUC
52 #A =
7
# B =
d 122-B
22
# c 9
=
4
# (A nB) =
# (Anc) = # (BC) =
3 2
4
# (AUBUc) =
1
# u =
20
, # (tubuc) =
1 + 2 + 2 + 2 + 2 + 3 + 4
=
16
#(A ' nB'r2) =
20 -
16
=
4
Al B' Cl
A A A
B B B
2 2 2
↳ in Binc
A
B
2
# (AUB) =
4 + 4
= 8
AUB (AUB)
A A
B B
>
-
2 2
6
⑰
100 8
x
108
goo
* (B) * /39
15 45701590265585
585
457115
# U =
1000 # (D + =) =
#DrB)UsDrA100-15
# D =
100 # (D1B) =
70
# D'
goo
=
AID
2653355
#
go
=
# B10 =
# (AUB) (D =
1000 -
505 -
100
315
=
4. (AID) (BID) =
10
-
-
