Rachunek zbiorów, Matematyka, Ćwiczenia
[ Pobierz całość w formacie PDF ]
,9>0>5-@#
,-/4<817>.59;?=
*
0
/%('.$",.*(&)$!,$++$#/'-'&)$
# " :MN<PMQH=JG(GO=$JL<RJ?KJPD@?ID@JFL@UMG@ID@N<F!<=QORQMF<U>R?<ID@KL<P?RDP@-
-$("!NRI"$E@MN R=DJLOGD>R=><ZFJPDNQ>C.
.# .#!$ !NRI"#I<G@
V
RQ?JKLR@?RD<ZO.#!$ ,
/ !!NRI"R=DYLGD>R= E@MNKJ?R=DJL@HR=DJLOGD>R=LR@>RQPDMNQ>C.
0
!
!NRI"
!
E@MN R=DJLOGD>R=PQHD@LIQ>C,
1* /#!$!%0!NRI"R=DYL E@MN R=DJLO/#!$!%0,
21 /1!2!30!NRI"1E@MN R=DJLO/1!2!30,
3/10 /1!2!30!NRI"/10E@MN R=DJLO/1!2!30
# # :MN<PMQH=JG(GO=$N<F!<=QORQMF<U>R?<ID@KL<P?RDP@-
-# ,
./#0 ",
//#!"!#0 /#!"!#0,
0 ",
1 /!"!!0,
2/*0 /*!#!#0,
3* /*!#!#0,
4/1!20 //10!/1!20!/1!2!300,
5/"!%0 ."!%/,
6"!# ."!$/
# $ :MN<PMQH=JG(GO=(N<F!<=QORQMF<
U
>R?<ID@KL<P?RDP@-
-" ,
.$
& ,
3
#
!
",
4
!
#
",
5" ."!$ ,
6$ ."!$
3
,
/ ,
0312 ,
1
3
$ ,
2
 % *0/%('.$",.*(&)$!,$++$#/'-'&)$
# % 9ROK@ZIDEKJID
V
RMR@R?<ID<!O
V
RQP<EW<>MQH=JGO-B?QKJ?<I@R=DJLQMW<LYPI@ JL<RMQH=JGD$D%
PKLR@>DPIQHPQK<?FO-
-'!# /7 (!+7 !#0,
..$!!' /7 (!+7 "$0,
/%!' /7 (!+#7 "% 0,
0."!#/ /7 (!+7 ""-7 !#0,
1"!# /7 (!+7 ""-7 "#0,
2" /7 (!+171-'0,
3/7 (!+7
"#0 /7 (!+171"#0,
4/7 (!+7
"$0 /7 (!+171"$0
# & :QRI<>RPMRQMNFD@KJ?R=DJLQR=DJLO0-
-0-*,
.0-/#0,
/0-/1!2!30,
00-/#!$!%!&0,
10-/*!10,
20-//#0!/#!$00"
3<F<E@MNR<G@VRIJUMU>HDW@?RQGD>R=W<@G@H@INYP?<I@BJR=DJLO<DGJUM>DW<E@BJKJ?R=DJLYP/
# ' :QRI<>RKJ?<IW<MOHW@R=DJLYP-
-/"!#0+/$!%0,
./"!#0+/"!#!$0,
/+/#!$!%0,
0"!$ +#!!' ,
1"!$ +.$!%/,
2"!$ +."!%/,
3!+."!#/,
4*+."!#/,
5."!#/+."!#/
# ( :QRI<>RKJ?<IQDGJ>RQI>RW@UMU>PMKYGIW< R=DJLYP-
-/"!#0,/"!#!$0,
.,/"!#!$!%0,
/"!$ ,#!% ,
0"!# ,.#!%/,
1"!#/,.#!%/,
2!,."!#/,
3*,."!#/,
4."!#/,."!#/,
5#!!' ,.$!!'
# ) :QRI<>RKJ?<IW<LY
V
RID>W@R=DJLYP-
-/"!#02/$!%0,
./"!#02/"!#!$0,
/2/"!#!$!%0,
0"!$ 2#!!' ,
1"!# 2.#!%/,
2.#!%/2#!$ ,
3."!#/2*,
4*2."!#/,
5."!#/2."!#/
# * 2G<?<I@BJR=DJLO%PQRI<>RE@BJ?JK@ZID@ID@?JR=DJLO!!NRI"R=DYL%
-!2%-
-%-'!# ,
.%-"!$ ,
/%-."!$/,
0%-*,
1%-!,
2%-#!"/+/%0,
3%-'!$ +$!!' ,
4%-/"!#0,
5%-
# "! :QRI<>RR=DJLQ-%+&! %,&! %2&JL<R&2%!E@UMGD-
-%-."!$/! &-"!$ ,
.%-"!!' ! &-."!#/,
/%-'!#/! &-#!!' ,
0%-.$!#/! &-.#!'/,
1%-'!#/+%!!' ! &-/#!"!%0,
2%-'!#/+.%!' ! &-"!&/+.(!!'
%"8<>COI@FR=DJLYP &
# "" :QRI<>RKJ?<I@R=DJLQ!E@UMGD%-#!% ! &-.$!&/D'-"!!' -
,
.%,&+' !%,& +'!%+& ,'!%,& +%,'
!%+&
! %
,&
! %
+&
4NYL@RPQRI<>RJIQ>CR=DJLYPMW<LYPI@/
# "# 9?JPJ?IDE!
V
R@?G<?JPJGIQ>CR=DJLYP%!&!' $ 0R<>CJ?RW<LYPIJUM>D-
-%,&
-%
+&
,
0%,&+' -%,& +%,' ,
1%+&,' -%+& ,%+' ,
2%2&+' -%2& 2'
.%+&
-%
,&
,
/%2&
-%
+&,
# "$ 1RQ?G<?JPJGIQ>CR=DJLYP%!&!' $ 0R<>CJ?RW<KJID
V
RMR@LYPIJUM>D/9R<M<?IDEJ?KJPD@?UR"
-%2&,' -%2& ,%2' ,
.%+&2' -%+& 2%,' ,
/%2&-%
+&
,
0%+& 2&-%,
1%2& 2'-%2&2' ,
2%,&2' -%,& 2%,'
# "% :QRI<>RR=DJLQ-%+&! %,&! %2&JL<R&2%!E@UMGD-
-%-."!$/! &-/7 (!+17#1"#0,
.%-"!!' ! &-/7 (!+77# !"0,
/%-! &-/7 (!+17$1!%0,
0%-/7 (!+17!#1"#0! &-/7 (!+17!#1!%0,
1%-/7 (!+7
!$7%-"0! &-/7 (!+7
!$7%""0,
2%-/7 (!+7
!$7!#!"0! &-/7 (!+7
!$7!#$"0
# "& :QRI<>RKJ?<I@R=DJLQ-
%-/7 (!+171"#.171 $#0,
&-/7 (!+171 $#-171 $%0,
'-/7 (!+7!$"". 7
$ #.&7 "%0,
(-/7 (!+7
$#. 7
!
$#. 7
"
$#0,
)-/7 (!+7 $#-171 $%0,
*-/7 ("+#" 171 "'0,
+-/7 (+#" 171 "'0,
,-/7 ( +7
!&7-&0,
--/7 (!+7
!&7-'- 7 ""0,
.-/7 (!+7 $#-1$71!&- 7
$'0,
/-/7 (!+7 $#-1$71!& . 7
$'0
# "' :QRI<>RI<LQMOE R=DJLQ-% &! & %! %
-% %JL<R&
-& &!E@UMGD-
-%-/$!%0! &-.#!& ,
.%-/$!$!&0! &-#!!' ,
/%-.#!$/! &-#!'
-%,&
' *0/%('.$",.*(&)$!,$++$#/'-'&)$
# "( 9?JPJ?IDE!
V
R@?G<?JPJGIQ>CR=DJLYP%!&!' $ 0R<>CJ?RW<LYPIJUM>D-
-% &+' -% & +% ' ,
.%,& '-% ' ,& ' ,
/%2' &-% & 2' &
# ") 4NYLQRKLR@?MN<PDJIQ>CKJID
V
R@ER=DJLYPHJ
V
RI<KLR@?MN<PDU>PKJMN<>DDGJ>RQIOF<LN@RE<UIMFD@BJ/
%
y
)
y
2
1
1
1 2
x
-2
1
x
&
y
*
y
2
1
1 2
x
-
2
2
x
-2
'
y
+
y
4
2
1
-3
-2
1
3
x
1
3
x
(
y
,
y
3
1
1
1
3
x
1
x
%"8<>COI@FR=DJLYP (
# "* 6<MRFD>OEKJ?<I@R=DJLQJL<RJKDMRDI<MRFD>OED>C?JK@ZID@ID<?JKLR@MNLR@ID!
"
%-
!
7!8 (!
+ 8-7
"
,
'-
!
7!8 (!
+ 8 !171
"
,
!
"
!
"
&-
7!8 (!
+ 8 " 7
,
(-
7!8 (!
+ 7
!8
"&
# #! 6<MRFD>OEKJ?<I@R=DJLQ"3@
U
MGDNJHJ
V
RGDP@R<KDMRE@PKJMN<>DDGJ>RQIOF<LN@RE<
U
IMFD@BJ"
%-/7!8 (!
+78 $"0,
&-/7!8 (!
+7!$
!8#
-#0,
'-/7!8 (!
+7!$
!8#
-"0,
(-/7!8 (!
+7
!8
$7!$8 "$0,
)-/7!8 ("
+7
!8
$7!$8 "$0,
*-/7!8 (!
+171!181!%0,
+-/7!8 (!
+7
!7$!"0,
,-/7!8 (!
+181 $$0
# #" :QRI<>RI<MRFD>OE R=DJLQ-%+&! %,&! %2&JL<R&2%!E@UMGD-
! &-/7!8 (!
+8 $ 7
!
0,
/%-/7!8 (!
+8
$8 !"0! &-/7!8 (!
+8
$8-"0,
0%-/7!8 (!
+17#1"$0! &-/7!8 (!
+7#
!8
!&0
!
7!8 (!
+8 ! 7
!
"
# ## :QRI<>RI<MRFD>OE KJ?<I@R=DJLQ-
,
'-/7!8 (!
+7
!8
!$7!$8!#!"0+/7!8 (!
+7
!8
$7$8!#!"0+
+/7!8 (!
+7
!8
-#0,
(-/7!8 (!
+8 $ 70,/7!8 (!
+8 "$70,/7!8 (!
+171!$0,
)-
/7!8 (!
+ 8 " 7
!#0+/7!8 (!
+ 8 !#1710
,/7!8 (!
+181 "$0,
*-
/7!8 (!
+8 !7
!$70+/7!8 (!
+8 !7
$70
,/7!8 (!
+8 "171$0,
+-
/7!8 (!
+7
!8
"(70,/7!8 (!
+7
!8
$&70
+/7!8 (!
+7
!8
!$70,
,-
/7!8 (!
+7
!8
!&02/7!8 (!
+ 7
!8
!%0
+/7!8 (!
+8-7
!$0
# #$ :QRI<>RI<MRFD>OE KJ?<I@R=DJLQ-
%-/7!8 (!
+$7
! 8 !%7
0,
&-/7!8 (!
+8 $ 7
- 7 $ 8
0,
'-/7!8 (!
+8 ! 7
-7
!8
!$8-7 $"0,
(-/7!8 (!
+8 $ 171. 8 !#17#10,
)-/7!8 (!
+7
$7!#!8
-". 7
!8
"$70,
*-/7!8 (!
+8 !
$
7
$. 8 $$
$
7
. 7
!8
!#0,
+-/7!8 (!
+7
!$7 - 8 "% . 8-%0,
,-/7!8 (!
+8 $ 7
!#. 8 !7
# - 7
!8
"#0
-%-.$!$/ ."!$/! &-! #!&/,
.%-
%-/7!8 (!
+8 $ 70
,/7!8 (!
+8 $
7
0,
&-.$!$/
2/7!8 (!
+7
!8
"&0
Â
[ Pobierz całość w formacie PDF ]