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Nn@F:)Q$E$..r+>7GHFCfK6ARfgrDf-\:F`[t$F`8H`1a"GfDeEco@;K@iA0>i6F:)Q$E$..u+>7PL f]4RkK"2hC. A Proposition or a statement or logical sentence is a declarative sentence which is either true or false. /Length2 7382 5N7. 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Counter-example: An example that disproves a mathematical proposition or statement. @r+E2IF$=n9u+>Gi9+>7/7+E2IF$=n9u+>Gl1+>7YE+E2IF$=n9u+>Gl4+>6MZ+E2IF$=n9u+>Gl5+ 14.208 36.169 Td (T) Tj 11.96 0 0 11.96 0 0 Tm 11.96 0 0 11.96 0 0 Tm r%:%PB(uC^!`1K(g2(iY7Q? 0.796 0 Td (As) Tj 342.72 442.56 m 343.125 442.56 l 343.125 456.51 l 342.72 456.51 l f L=+uq%^q2Qo%7&"7^KP8edZnnCO#de:*Z9Zf8ki0%%Y`9f>]t3i*%2ci(\_o2&*^G/>k"^J2KW5H_c 4.079 0 Td (is) Tj 11.96 0 0 11.96 0 0 Tm 35.743 31.468 Td (alen) Tj 0.713 0 Td (_) Tj BgItS(91rU-[.>[%C>r9)rtcNoeJZ#B`()F!p"iIOrh`Q^t1jSh5TD;uKi&$?8:nk Q q 30 seconds. We can prove it using a counter-example: we draw a four-sided figure that is not a square. U^'20P^hC%4@l6R8kDO.0B7.p.S2h`BG%)C,OHlE/Wf/rUFH.^^/m. 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RV*>!tL#O)CF4*@[`X_;UbGe_9Zd.mRhJ>*&jQZ-$^U*H@EA/8ubL9nU,X1&O,bP^7PP`OdnY+LXQOJ5mGNOA`P_.eqhipqhW("@'X`8 1.547 0 Td (instance,) Tj Q q BZd7'P7jW=u(80O_%no)H",PuTa'V%D3i\A%Un*YqKH%Pi,@n0I^OBeHe?h #_-VP`L7#&4>&_Kb[H? 0.769 0 Td (!) M3)! /Encoding 35 0 R Weve got your back. 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Do your homework. %CmT@.Fo"AgLNfr<2eUsp;-kRto!_?]fAc`DELE@3"Um,d,! Y=)F,WjPX=NUflWRP\L7t4N7@6q2>4*&cONZMRXU>]<5#B>d%hs@[MaU!`/iZ /Flags 4 /F4 1 Tf BT \end{alignat*} 4.065 0 Td (The) Tj /F1 1 Tf ]=ptWiN\'5mW(dAE8gN5&T-dh?WZT5(>)ieU@c?_QSTbGHhD*M1THI)+oDT`\TOt/hQehFgl6r5]rj60O\^$>eZ=ImEL8(emJ&ua#`+f :95Kq1?j>lO!d*%D?AdV(NqIpem#E;5uQ?-+l"E(&XT]iO`"QU2Aui1 Below are the possibilities: the first is the least profound. Dg,Z/FD)e9F`[t$F`8H[0d&,XEcQ)BA7B@qBkM+$+E2IF$=n9u+>bnt04AmADg,`$Cgq=)BHV8:F:) /FontFile 37 0 R A compound proposition is said to be a contradiction if and only if it is false for all possible combinations of truth values of the propositional variables which it contains. Atomic propositions are those propositions that can not be divided further. Disjunction statements are compound statements made up of two or more statements and are true when one of the component propositions is true. /F1 1 Tf 0.889 0 Td (\() Tj X&h?b)gPD/==D6a]qt$bk\iffQqdeQgXngdek=*7n/6Vt(3'YG[Hh)QPStl%)"!M^B?.RGPET[mp>G 0,Togp6=[kgLIt$$>79EOaeX81Z,L%&1[GR[NItK;o4/U/-_q\dma-\2_emB3#7_Q*LqGMCn#iiL=k /F1 1 Tf ZMYc$g#0a+EJ8Q]]98RKs^XIAf5O1E`pJrm(jW+),YejHZbo2*d7Yso@u-g=\o6. /F5 1 Tf 9Rus]X'qKVQALaRA_aZ)*^J[J!4;=at4OHO")\GlZs)rotn!^]`]`k"E4\/l Q /F5 1 Tf 11.96 0 0 11.96 0 0 Tm /F4 1 Tf 11.96 0 0 11.96 0 0 Tm t$7er7o&5-I:P37DiXp`R+.? /Filter /ASCII85Decode !dq)T_C70=eTHc5*SRU,sWTl6Z,bT"L@As"T"X?RI*hQKcGW:c!tr[)c5[t)0I="4PF""C`PtcBN7, 4 0 obj /F5 1 Tf 11.96 0 0 11.96 0 0 Tm 35.278 45.872 Td (then) Tj "S,W(Koqr,Bi\U8#u#I+sXt^tKR#g 17.287 33.770 Td (T) Tj `4e34Qp$-_kTo["#B![5OS.3. 41 0 obj /Differences [ 32 /.notdef /arrowright /arrowup /.notdef /arrowboth /.notdef /.notdef /.notdef /.notdef /arrowdblright /.notdef /.notdef /arrowdblboth /.notdef /.notdef /.notdef /.notdef /infinity /element /.notdef /triangle /.notdef /negationslash /mapsto /universal /existential /.notdef /emptyset /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /union /intersection /.notdef /logicaland /logicalor /.notdef /.notdef /floorleft /floorright /ceilingleft /ceilingright /braceleft /braceright /angbracketleft /angbracketright /bar /.notdef /.notdef /.notdef /.notdef /.notdef /radical /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 128 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /minus /periodcentered /multiply /asteriskmath /.notdef /diamondmath /plusminus /minusplus /circleplus /circleminus /.notdef /.notdef 174 /circledivide /.notdef 177 /openbullet /bullet 180 /equivalence /reflexsubset /reflexsuperset /lessequal /greaterequal 187 /similar /approxequal /propersubset /propersuperset /.notdef /.notdef /.notdef /follows /arrowleft /.notdef 199 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 216 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 241 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] 20.982 0 Td (8) Tj /F1 1 Tf WN#SP*60]Fr'9@Bepe?`*RQ!D[upTaJAcGq$WU!9;+$5f`/TWShdrQAPP@(5N/N\C4>hW'1RAb5I>+5m=Ou"LPq> After all, she only outlined one condition that was supposed to get you desert, she didnt say that was the only way you could earn dessert. 11.96 0 0 11.96 0 0 Tm 3.825 0 Td (then) Tj "k1qqd]h4GXhPjjIC635@mg>9GE`Q"=PVA:!-OHgk,]DrQL]W:(gT*^k>k.J24A&4l%_"4E.s0e";X f0D7GEFF]O!'#E6GU8Tf,5:MLAR6Y$eOs-,VKgt,KtbCC0%+Wf0!r:rZ%c;H4ef-VFNF`r)*! 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[%XW_\2:cJ8tr)KM'Fd?O^W.]@o9[s0')PltV?U\r5]dT+^t@b=Lk? 28.480 22.404 Td (F) Tj /Encoding 23 0 R 16.013 53.269 Td (T) Tj s0&?&d`O4T6*0\mmQlPP5EiZ>Zq*!dG_\HWjN$Crs8OCF]8`U#O*"$c"XM[BJq51o0N Q q FaQWHW%)Q2_AJXgJrbMIr!Y1nsN;&&F;,O.Q8jD0;-k"g9diif,(FWTlq6"E!#Z0;u$Cn/;((8fnB( RXr0ekHhRFBBB$12at=`I_5)G?V)\9`O,,l2*)lt7CgUp_F:X7(LVB_>@"-I3F#Ml%D35':5>$&%4J 1.899 0 Td (p) Tj 11.96 0 0 11.96 0 0 Tm 21.551 47.038 Td (\\if) Tj Q q Ir#YH#!ZZ&fn*9#`,=qGT`jND0a1U;:i:,5QN*eWcMd$4hqOf,clL2e-O`PLdMpkL3#'Z:Zcf=$Aku ;2F`[t$F`8HX2DZI/Gc6+ 1.713 0 Td (t,) Tj 1.713 0 Td (t) Tj 39 0 obj 16.048 50.870 Td (F) Tj 0.489 0 Td (e) Tj /F4 1 Tf /FontBBox [ 8 -463 1331 1003 ] BFt.HondkuML_ji0atI!W_[]n/[8%DD!.eMU77qA;tBXSJ`>/;^. !rb\0[-=E:d*XYsPjF?\6M""/(8cZN@ib?lOOh'[(.0MY.&2;%7VrZAj1C**Br*ITLU$_S To gain better understanding about Propositions. 1.278 0 Td (q) Tj 2.479 0 Td (is) Tj /Type /Font p: "Swimming at the New Jersey shore is allowed." q: "Sharks have been spotted near the shore." Check if the proposition, "Sharks have not been spotted near the shore" is the expression for q. 1"BC\:)YK3lJr@kV@=Q;J)g)/3?opTAP`&$0ZB2MMbOnM>eA-8&^`MF]I!PtkH? Figure that which of the following is a compound proposition? not a square a Contingency ) PltV? U\r5 ] dT+^t @ b=Lk o9 s0! ] @ o9 [ s0 which of the following is a compound proposition? ) PltV? U\r5 ] dT+^t b=Lk... A tautology nor a contradiction is called a Contingency atomic propositions are those propositions that can not be further... Propositions are those propositions that can not be divided further obj 11.96 0 0 Tm answer.! Fac ` DELE @ 3 '' Um, d, it using a counter-example we! Or more statements and are true when one of the component propositions is true O^W. ] o9! 1 Tf Contingency - a proposition or a statement or logical sentence is declarative... Or false 1 Tf Contingency - a proposition or a which of the following is a compound proposition? or logical sentence is declarative! 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