a,~~ ~f}math.uni-pannon.hu/~lhorvath/1.pdf · q,. ~ ~~a.t;(.a ~ ~ jw.t~ rl,tfai ~u' (q-m~.. dt...

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C. .,~ ~__n!._' lf r ~elYUL ) I'~~ ~. ~ A,~~ C ~rnl-~. ~F} ~ a. A= Au(An1J\" -8-. (An1)C)U:B'" AUD, c. (Au1)')n1/= A\'B1 c- eL. (A UB) n (A n'i» ;: (A\!)) U{13\A), e. A u ( 1) ne) -= (A UD) n ( AUC') I ~. A-n(J3Uc)= (AnB)u (AncJ. J , r, 2. T~~ ~ cuz. A,S eh C ~m.RjL2fdkd cvz- ~ ~rn.e~~ ct-. ~ ah.. A JU)~~iL k J -B-. OJL A fu ct 1> Jk1.;j~~L1 k ci. C nLfYL) c. ry/;i-rui CL ~ ~d ~'1Xl~kl ct. eL. ~ ~~d .l?-Ozi.i.1 ~CUL Q}L ~~ !o'rv-d~k. .k J t . ~W Qfl- ~ k- 1-D~ buJ.. k) f. ~l ~~ny ~~m..kö.t>dkvU{. k) ;J. ~ ~ ~.~ kk-O/[)-d~k.. , 3. ~ ~F~!kYl, ut lift ~. Hz A ~(j jw~0e cvd;) k~ ~. m+~ ~ CV~dP~ lift ~dLt / ~ 'D ~.~ YUJ r-ec1ifJ CW ~ Q ryu{~1Yct(J- ~~'cP.Lk-. Ta-rL;ncuv7:.-Q ~ / ~t. j-~~ CL 1;)~~ ~~~: 'c Q. ':B, pr. AUD) c. An~) <a-. CA n :o) G) ~. CA \ 1)) U (:B" A') . ~ . ~ ~dd~ ~ Fnfi- tcL~f tV1LrL. A z A ~ern.l- rVJ iiu~ <?- wa I .~ ~ ~~ ~ cvz- ~/;- F~td* ~~iL / eL 43 ebe, ~ YUj cvd I b::rn ct ~':> ~h.- nu1. k;o dL f.L/ 4- C ru- ck~ wd ~ :n CL ~~ ~ LD.~ k. t O-rJ- ~ ~ I rYU- t ef fuz-kflJ fl 'VlIJOJ,. CL !:;rvd~ ~rrv...'T~: ú. . Au~ Uc ) .fr. A n 17 nc, c. . A c u 1? c U c c.) eL. A c- n 13 c. n c c) e. A n 1) () C c) t . Ac n tp, () eG) ~. ('An ~ ') U CA nc) u ( J3 nc') . c eL. AnB) e. A"B ) f. (A U1))c)

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Page 1: A,~~ ~F}math.uni-pannon.hu/~lhorvath/1.pdf · Q,. ~ ~~a.t;(.A ~ ~ Jw.t~ rl,tfai ~U' (Q-M~.. dt b-al~ ~ pr. ~ 0< fA> f:L ~ A. tj~ j ~ &~k.-~CtA'L ~ 0-. ~ 'P: J/;~ [0(4] ~~ ~k)

C. .,~ ~__n!._' lf r~elYUL ) I'~~

~. ~ A,~~ C ~rnl-~. ~F} ~a. A= Au(An1J\"

-8-. (An1)C)U:B'" AUD,

c. (Au1)')n1/= A\'B1c-

eL. (A UB) n (A n'i» ;: (A\!)) U{13\A),

e. A u( 1)ne) -= (A UD)n ( AUC') I

~. A-n(J3Uc)= (AnB)u (AncJ.J , r,

2. T~~ ~ cuz. A,S eh C ~m.RjL2fdkd cvz- ~ ~rn.e~~

ct-. ~ ah.. A JU)~~iL k J

-B-. OJL A fu ct 1> Jk1.;j~~L1 k ci. C nLfYL)

c. ry/;i-rui CL ~ ~d ~'1Xl~klct. eL. ~ ~~d .l?-Ozi.i.1 ~CUL Q}L ~~ !o'rv-d~k. .k J

t . ~W Qfl- ~ k- 1-D~ buJ.. k)

f. ~l ~~ny ~~m..kö.t>dkvU{. k)

;J. ~ ~ ~.~ kk-O/[)-d~k..,

3. ~ ~F~!kYl, ut lift ~. Hz A ~(j jw~0e cvd;) k~ ~.

m+~ ~ CV~dP~ lift ~dLt / ~ 'D ~.~ YUJ r-ec1ifJ CW

~ Q ryu{~1Yct(J- ~~'cP.Lk-. Ta-rL;ncuv7:.-Q ~ / ~t. j-~~CL 1;)~~ ~~~:

'c

Q. ':B, pr. AUD) c. An~)

<a-. CAn :o)G) ~. CA\ 1)) U (:B" A').

~ . ~ ~dd~ ~ Fnfi- tcL~f tV1LrL. Az A ~ern.l- rVJ iiu~ <?-

wa I .~ ~ ~~ ~ cvz- ~/;- F~td* ~~iL /

eL 43 ebe, ~ YUj cvd I b::rn ct ~':> ~h.- nu1. k;o dL f.L/ 4- C ru-ck~ wd

~ :n CL ~~ ~ LD.~ k . t O-rJ- ~ ~ I rYU-t effuz-kflJfl 'VlIJOJ,.

CL !:;rvd~ ~rrv...'T~:

ú. . Au ~ Uc ) .fr. A n 17 nc, c. . Ac u 1?c U cc.) eL. Ac- n 13c. n c c)

e. A n 1) () C c) t . Ac n tp,() eG) ~. ('An ~ ') U CA nc) u ( J3nc') .

c

eL. AnB) e. A"B ) f. (A U1)) c)

Page 2: A,~~ ~F}math.uni-pannon.hu/~lhorvath/1.pdf · Q,. ~ ~~a.t;(.A ~ ~ Jw.t~ rl,tfai ~U' (Q-M~.. dt b-al~ ~ pr. ~ 0< fA> f:L ~ A. tj~ j ~ &~k.-~CtA'L ~ 0-. ~ 'P: J/;~ [0(4] ~~ ~k)

5. ~ (Q I clL, 1» .~ ~z1~~ rnvzlr. tj~J.~Q-, Ae Jt ~ <P{Ac) == A- 'P(A))

~ A,BE&. ~ 'P/AU'B)=-'P(A)+'P{13)-1'{AnB)) J, T(A\B)=='P(A)-'P{An13),,

c, AI íj} C é Ji ~ 'PCAU13uc);: 1/{A) + 'PCB) + 'P(c) - 'P( An '13)- 'P (Anc) -"P(13nc

+ 'P(A{)'Bnc).

6. ~ ~~ ~~ ~Ot>~ A( 1> ~ c ~~~ 1eJ.i,J, --1- '1 r' 1I.I,..,Oj,,' .+.0-

~ a- M-ve{,};Z~ 1l.rO.1o~~o""" /lÁ~:

i. ?(A):::O,Sj 'PC1))=O,bj 'P(e)::: O,4i 7(An1:»;:. 0{3; tp (13()c') = O/AS; 'P(A()c

>=O, A, 'P (An'B()C);: 0,05.

.ii. 'P(A):O,8j rp('B)~O,5; 1"fJ.(C)AO,4i 1'(An'B)=ú,'ti 1'('13()c)==o,2.i '1>(A{)C)=.

co O{:3.2.; ?(AI)'8{)C) '" O, AG.

ct, Ar ~ ~ ~~~~~ ~U / CLmL~ Q. ~ mt'D.' fil rl'\{)Jb. ' """"'.l"Jb /1~P,".l'YljJj)l].4.' f

m/:>~~o'- e~,~~-- 'v~"~a Ir,13 v:.. C ~i'r'"U-~.

{T, ~ QJZ, ti, ,- rJ1 tp(A)::: O{~ j ~ .J-e-B-B-L ~~d~i~ f-€-diJ m-dl-~ ' ULt ffl.-&n.cR..A~Dt}u-rvk.dkK. ev;z:.~ ~ Q, -~ ~md~~

r T

C . SZ.D:Á1'Uo)~Q. ,~ :

J

(;1' rp{AC) (..2.' '?(AU13) C.3' ?((A U:oy:') Cit' 'P(J?/nCC)

CS' 'P(Ac UeC) Cb, 'P(:J3'C) C:f' rp(C'-A) c..!Jo 1'( AUB UG)

C-S' ? ( (A \]3) U(~>', A\) C.,o' "p ( ( A~B) VC) .

':fo ~ A, 1) J C ~:D ~ kJ.~) a~~ f~kl.dd.i~~tJl~p»h~ 52;: AU.BuCu:D.

0-. Ar r'r1-UJ cvx- A, ~I C ~ 7> Aa1~ deJal ~f}; Q.- ~&, b-al~.

,~. rlO~I1f)1/1 O~ f4) fiL) r-~) flt) QfYli,PlltJ~h-I' ! fi, =;f. ~~J ~ ~-~ 7""-'~ '1.=1

'A. - . O. "..,...,.,.,~ ~ . í} JA (í) .ll. - - lJ_r , tr I , P'lL~ R.- dtAO', ..,~a:.,n. ~ ~ ~ ~ r: v~ ~ r..O( ;<f] (1)cu.o6'Z<,;~.e. ~ /'Yl.R...~ J

~~ 'P(A)~{'--A) 'P{1;)=:f.2.} ?(C)=f'.; eb ?CD)=fLlf'

8 . ~ "-""- 4, 33 ..;, §t.. k..P.~ I Q ~Pure- Af) 1'> 1 <1) A () 'J?/ f <fi). . , ,

Ac.n 1!>+ <fi)'~ A lJS ~ ~ .

Page 3: A,~~ ~F}math.uni-pannon.hu/~lhorvath/1.pdf · Q,. ~ ~~a.t;(.A ~ ~ Jw.t~ rl,tfai ~U' (Q-M~.. dt b-al~ ~ pr. ~ 0< fA> f:L ~ A. tj~ j ~ &~k.-~CtA'L ~ 0-. ~ 'P: J/;~ [0(4] ~~ ~k)

Q,. ~ ~~a.t;(.A ~ ~ Jw.t~ rl,tfai ~U' (Q -M~ ..

dt b-al~ ~

pr. ~ 0< fA> f:L ~ A. tj~ j ~ &~k.- ~CtA'L ~ 0-.

~ 'P: J/;~ [0(4] ~~ ~k) a.mL~ 'P(A)-{'-4)

1>(:5);:: f:L ~ 'P (A ()J3).~ f4f-2- . I

/ A 1. ~ ~M ct- rrurt~.;

3. Q. ~ 1>{A)=~ ~ 'PtB)= ~. l'j~rJ ~ 1z:f~(AJ)13)~t

.B-. tj~) ~ 'P{AI113)~ mLn. (PCA),7(1»))) el:, 'P(AU13)~ 'P(A)t-'P(:B).

Ao, ~ JL ~ X Jwl~ 6-a1.~) ib ~ ~CX, <;IfJA-'

Uj>-J ~ ac ;]3'0 [AO~ I AeétJ ),d~dhzvr ~ !L-Mi-

b-a.t~. Mu..,taAbCL~) ~ !ieJt. ~ J3=fA€JtI AC:~}.. - .. L' - S .-1 ~ A€ A f\-(/)r-. 17-1 11J" j., í"r'nn

AA. ~ Ac1R ~ BI/CA'):.: LG; k ~$A' 'J~'-'~~<r--j """"'(j<JQ)Z

1R nr , 1/ II

('fR1~ ) ~) ~ tVZLW~~~ 1i1.Vz.o-.

12..~ (Q,JL,'P) ~ ~"'~~~~) ~ ~ J3eJC)

a.~ 'P(:I3» Q. ~ ;h. ~ fAI) 1> j Ae Jt. J ~ 'PJ! (A 1)13)' ~ 'P~~~~)

(AeJt). iJg=drJ ~ ct (p, i ;B)~) ~ ~-d~~ rrwz.6"