practice_problems_from_9-6

# practice_problems_from_9-6 - Exercise 9.5 Note in some...

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Unformatted text preview: Exercise 9.5 Note: in some eases, to shorten the derivation negation has been handled via direet rules {rather than by “pushing-in" intermediate steps). #1 1. V1 [311,513 —1- \$121.11)] .h. —-SEb,bJ = —-S{h.a} Given _ V1 {5{1,a} —I- Slf1.hj]=, -SGJ,1:II). - -S{b,a} |= J. {GEL} 3. V1[S{1,a} —-" \$1.133], -SC1J,1J:I. Sill?!) = J. {- -, = 4. V1[5{1,a} —i- SC1IDJ], 51:13.3) —i' SGJJJ), -uS{1J.b}. Slibﬁj |= J. (V. = 5.1. V1[5{1,a} —i- 3113], ﬁSEhlal. nSEbh). m |= _ (—-". I=J 5.2. V1 {S{1,a} —'* 31.5le], m, Sfbﬁ} |= J. (—i'. |=Il '9" #2 l. V11 5111,11) = Elf; 5{1,v} Given 2. Vu S-Eu,u}. —-Elv S{1,jv} = _ GEL 3. V1.1 5mm}. -E|v Sling-'3 |= -_ Substit. of free variables 4. V1.1 S{n,u}. -E|v S{a,_v}. - 511513;] = J. (v3. H 5. V1.1 5431,11}. Egg. -Elv Stay), ﬁle} = J. (V. =J 1." #3 l. = V1 [—qu1} —1 E|_v (PEI) —-* Rﬁvlj} Given 3- * V1 [113(5) —=' 33’ {Pi}? —’ Rﬂ’m = J— CC}— 3. - [ePfal —=- 3? (Pit?) —r- Rivﬁﬁ} = i (49'. = 4. ~PtaJ. e33: {Pii’} —=' Riv}? |= J— {e—‘, = 5. —P(aj, —-EIv{P[1-‘} a ltd-'3). -{P[a) —:- mm = J. (e3. |=ir '5- ﬂdl,v3}'{PE1~’}—’ RETJJ. Hal. vREa) = J— {v—‘*, =J V! #4 l. = 31V}? 31.3?) v VxElv—-S(1,vj] Given 2. —- [31Vv 5421,15} v V1ElveSE1=F3li = J. GCL 3. eElev SE13): — VxElvﬁ SE13} = J. {—- v. = 4. —E|1Vv Stile}. — EI}=—-S{a._v} = J. {—-V, = 5. —E|1V}-‘ 3(13}. — Vv Stag-j. -Elv- Stag) = .. {—EI. |=]I e. —E|1V1e sum-31. —-S(a,b:l. -ElvﬁSEa,_vJ = _ (49'. = T- 5319'? SEXY): ﬁght. v3}"'5Ea,}’},i-Iﬁl = i (e3. l=} w" l. '11:ij 1: ﬁ‘ﬂ'xRix) = Elx [Rﬁxj —1 Pﬁxj] Given 2. VXPJZXJI V —-‘U':IR{K}, —-Elx [REXJI —3- Hit] = J. CCL 3.1. VxPiix}, H31 [REX] —3- Pij] = J. ('9'. |=JI 4.1 VxPiﬁx}, Pia), -Elx [RIIIXJ H Pij] |= J. (1'0", = 5.1. s’xPixJ. Pia), ﬁx [Rm —1 Fish]. ﬁmia) —2- Pin] |= L (H. |=J 5.1. WEEK}, 33:, -E|x [Rm —: chj],R{a},;Pl*_a1|= J. (ﬁ—n, =31! 3.2. HVKREXJ. a: [Rm —:- Pm] = J. (V. |=} 4.2. mm}. -E|x [Rm —:- Pm] = J. (49', = 5.2. —-R{a}.. was [Rm —2- Pm}, {may —2- Fun] |= i (—3.. |=J 6.2. its}. as [Rm —2- Pm], Es). Hm} |= i (--*.|=J v #113 1. Elx'ﬁ'ﬂﬁlﬁxg} H 5:35)] = EIzI‘u'y'SIIxﬁI '-.r ‘9'}'—-SI{::.§£:I] I. Easy-{Sing} H Sinai]. -Ellr.["i"}r5(3.}'} "I" IVY—'35.?“ I: J- 3. Elx'ﬁ'ﬂSEXJ-‘h H Sixﬂ]. V1-["i"3-'SI{I.1.'} 1; 'ﬁ’y—u S{x.}']] I: J. 4. Vy[S{a.}r} H S[a,a}]. ‘u'xﬁ [Virslixs'] v 'ﬁ’1-'-5|Ix.§r‘3|] |= i 3. Vﬂﬂlﬁay} H SHAH. Vic-IWySIILY] ‘2 Wyn-Sillin- *[Vi'sfli'l V VPHSEEJH i= J- 6. Hﬂﬂlﬁay} H 5(a.a}]. ‘u'x—-['dyS{x.§;] u 'ﬁ’y—ustxqr‘l]. w‘d'jrSIIﬁaJ} a —-"n"}r—-S{a,3r] l: J T". Hﬂscay} H sum]. Hxﬁwysm) u Hyﬁscxsll ijrSIIZaJ}, ﬁvyﬁsm; |= J 3. Hﬂscay} H 5mm. Vx-['ﬁ’1-'S{LYJ *2 VJHSEKJ'J]. Hrsiasl. ﬂswﬁtasﬂ = i 9- VEESERS} H Small]. Hr- [ﬁrssz v Hy—éﬁxqﬂ]. -S{a.hl Ely—- —-S(a.§r':' |= J- 10. WSW} e- 5(a.a}]. was [#1:st v vyﬁscxsll n3{a.b}. ﬂ satay} |= J 11. V1.*[S[a.y}H 5(a.a}].‘u'x—-['dy3{1.jsl v 'ﬁ’y—ustxaﬂ]. -u3{a.b}. Stu} |= J 13. Vﬂﬂlﬁay} H 5(a.a}]. Stab] H Susi. Vii-u [\$361133 'J 'ﬁ'y-u S{I.}'}]. - Stab}. Sﬁaxj |= _ 13.1 ﬁrming} H S{a.a}]. ﬂab}. 51:41.3]. 's'x—-["a"5:SI[z:.1.r} u 's'y—u 3113.13]. —-S[a by. Sign} l: _ 13.2 ﬁrming} H S{a.a}]. —-S{a,h}1 —-S[a_a]. Vx—-['ﬁ’y5{x.y] u 'ﬁ’y—u S{x.y]]. —-S{a.h}. Evian} |= J. l-l-.2 H}'[S(a.}r} H 5{a.a}]. -S(a.b:l. —-5{a.a}. Mags} H 5113.1}. "u’x—{h’yﬁﬁxg} 'u' HT—uﬂﬂxg-‘H. —-S{a.b}. Shy} = J. 15.2.1 H}'[Sl:a,1.r} H S{a.a}]. —-Sl[a,b:l. —-S§a,a§. S[a_c},ﬂ[a,a}. "dz—{VFSIILFII I: "ﬂy—uﬁﬁxgﬂ]. —-Sl:a.hj. S{a.c:l |= J. 15.2.: 's'y[3{a.1.r}H 5(a.a}]. —-S{a.b:l. —-5{a.a}. —-Ea.cl, —-S{a,a]. 'ﬁ'z—{b’yﬁﬁxg} 'u' ‘9'};—-S{z.1.r}]. —-Sl:a.h). 55a a! I: J. Given CCL Pushing in —. I11|=} EV.I=} Pushing in —. c»..|=:l Pushing in —- {xi} {1|=} I11|=} DH EV.I=} EH.I=} if EH.I=} EV.I=} (94:11.5 {94:} if“ ...
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practice_problems_from_9-6 - Exercise 9.5 Note in some...

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