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Logically, we can see that if two lines are perpendicular, then they must intersect to form a right angle. =DV$\@V7eIaB'A%dQOFYbt:hieFXHud>q#egCWlc+,RRpQ)Mloq4bKN>]f[p;fi._NV7CN+Ttg)>B< BT mW^S"S;#WPqO$6`F=1rDU^X/A@#"0C9j_)E0D bZJTE""!C4HD8bS3[)$6nNM[+@b;^bqq"Y5 0.713 0 Td (_) Tj Legal. /:^Sa-Fd3KHS2Tfk@*aGr:9f[\gApUjr`Pk_TaWY`nH"E>6?R5]%>FAA;>Wb[\@fjrH0@)i4etYElD /F1 1 Tf 1.775 0 Td (c) Tj 3.834 0 Td (equiv) Tj F`MM6DKKE'@rri)DIa)aF`MM6DKKK)Ch4`#AU%cr$CdP#B`VQl*@pejoYB!$=1ZZ-:^Xn4m?fd)TGG Ch74#+E2IF$=n9u+>Gf4+>7eUF^]G /F5 1 Tf '?%(gr;2`:;`C:Ol,uL!AV@8u7^nAbbV.WoOC*f! A proposition that is neither a tautology nor contradiction is called a contingency. /F4 1 Tf 29.081 38.568 Td (p) Tj :]".GrILVOV#P09c;rBi3OB+2`ZQoW%9Y?g'$e=eI7dfn5_LVr,]Y'M-/5CL)7H7+8s(j= /BaseEncoding /MacRomanEncoding /LastChar 255 )`/OP0ea_*/hm\Z,su]a@4%DF@oTANCqg3B8l.DKKqBG@bf++Co&)BkM?,+EV:.+@0jUEbT#lDBMY^FD,6&@ FBrm>\*(]il+b,unbTC]W_1Kd4K)T#)b3lgPjJ9WdmK+\oZu8c?eT?Q7!#iXcp#*=cIt1;585:@dN: /F4 1 Tf 1.774 0 Td (con) Tj sDQ%4=1b6bW^:6GA^m37QW$**%kVlImIYm4a+X@g/NmfN"bG$b_BOngXkqu,n@0@+N/'GccF(YXp'Z ;Tog;R'O7-M-^;n,XVG4,GUA^thD]]Cj`u?07@^(UeO 25 0 obj k?GoNV@ajr24l6b]H-5\h_@k1DA&CYUL!*8\)@oPCkXHo$ME>k!db^;f^P>]TmRo#? Q q 0.713 0 Td (_) Tj /F1 1 Tf \(1+1=2\) and "All birds can fly". /Filter /ASCII85Decode 6^J4%K'nM;bE8ElLptXLU3;c+=-!+Qudqq^%W7S7fE/2T8TPBfa;lU;")IHFKor9E@ST,1Jr#(65). 11.96 0 0 11.96 0 0 Tm 26.187 47.790 Td (Logic.) 1.014 0 Td (the) Tj ?5[kb64NgcX%ddp>Gr?$T'0PhuuDK`pSA/'"AjHN'^9a/aYQ6oh'\p(@^Y?RL5AmqopX+MdW:./?o_ i";'ir7YC07$"(u_8>rt.F@-k;A%d+[5f"FirOI_Q#qkK8laU^]Gfn[XP$eGW%Ae !gI@HL2:U8:VW9>Y SV;>I2DQqSi^H\@jqUjD:SQ2!pft@,0j^2]ZmHDA5"LAR%_XXjj_JBZU.M["m@K(h(aj:t9KGqq\FN 26.177 38.568 Td (p) Tj nm5p33R*%j9sVNP:C]*b&crr(d'b,WjC>neG9'E:)ZfO$M+\if+#J'L9[-MfQ. It is a proposition that requires the use of prepositions to form logic. Tj << B5(jaCi=>:E-670A9Di63B/-7Ao)C(Ebo7>CDf9Z:BkM+$+E2IF$=n9u+>G 2.446 0 Td (ositions) Tj Using De Morgan's Laws, we can express the negation as "I'm not eating out at a restaurant, or I'm not going dancing.". 1.278 0 Td (q) Tj ET Q q ?ASu75CD/E](E-670A9Di61c6C/BR+Q1ASrW0F`[t$F`8H[2BXYlATDL'A0>i6F:)Q$E$-tt "fa8W-KT"`_R@ooS=Y*D/BhZ4en2[,hZr@7igr^H+cn endobj 1.427 0 Td (for) Tj T>NkQL64.hgV8]+9!Zq-hGU3EFT,)YhBO+AEaGHjSeVWJ3?fWQHa"OZNfD! 0.713 0 Td (Y) Tj `(8$S;T@XQ@@Q;f6biXIfdRR&!\5pt_QG!Y/6FK5EGm7[dq[aS+\/]3*glBM[%P[J!kEmnSnI\k]R, NM!&HXuY2RSdahK,lgWA>dAS:*U4kN-U3F-QI?BasBm^,ZH43*)fl`B: !YJgrj5eeiXS-9Z.XTM)rkjG+96X^LZ%]0'8?AeQ:1:r25Bj/*!n0SRo, Note that for any compound proposition P, P is a tautology if and only if Pis a contradiction. 0.791 0 Td (seen,) Tj [n[LYLKP&asnWkIoG,gOA Continue with Recommended Cookies. >> 3.045 0 Td (equiv) Tj kTJK-D*P5e"#!Rh)@!i'(?e7J+G'c;ElF,%VdPj=pUu>8=^@AgQ0"9"?&S%;c&IQagglqWUlL#Qs$OAqr"cHL9Zp8?MWR#EM;F-SKO-D50=]k+Hc`N@foB3JY;5TD7oL-Vs Certain types of proposition will play a special role in our further work with logic. /F1 1 Tf /Flags 4 /StemV 20 1.798 0 Td (the) Tj ::m>[q[mlKC1PCeC$/F(7;(!qj0R<2"^W* KR3=7&T6Z6phEbT0"F^/he^sEb/ZiDf0B:+Co%q$85.mFD55r+=KTqE-ZJ=ol+>>E%0JO\(+>@(DEb/ZiDf0B:+C $2k(@#s%%CAcW^X8B]2?QC=R0/aqf,[U4?R$YMuLOAmP[nLlh-_J[CH3=Ft)Rqo+h8!sc8V`RQT%j ^id]3@J0LTru4(4+LX4n\FLHE@ihdIG)(EM@tKMLDOM0m9i_VK!lklS@ko]>\-<0Wg`U$r\ 176.64 249.6 m 177.045 249.6 l 177.045 263.55 l 176.64 263.55 l f @ 1.211 0 Td (instance:) Tj /Widths [ 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 667 333 333 333 333 333 333 333 333 333 333 778 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 611 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 778 778 778 778 333 278 667 667 778 778 333 333 333 1000 778 333 889 611 333 1000 1000 1000 833 833 333 333 417 417 1111 1111 333 333 500 500 1000 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 333 ] "^a[)FJc='cI!.C)!pLl:Z1G\pp:siH;BnUmV,_ t+d]_m*-9!VgUQ%7Qs^4\0/M2+>)^\[21/i#^r=S(R*`a(V+BHg9VGf [ /PDF /Text /ImageB /ImageC /ImageI ] 2.538 0 Td (exactly) Tj /F1 1 Tf /StemV 20 e6;Eu_8CL;gO/+H2M2ng_c-BS6WQ1K6eG'fcE!oX*G6q_K`id#!`O+j%;3VA4D]AOIX`',MUB_[^7H /F5 1 Tf /ItalicAngle 0 2.453 0 Td (that) Tj Examples of Propositions. @_2EJ^Q7SU`Vd/VG-c$!%e:P+LB?bJk4&r[b(;CZdqB=DG5 ]ccq*sm5Y%Ldka0XJWDQs`0`@f/OH-HCI"f^V4bS8lI@9bhi!Hi?QmNs;&t:#80Vup24f$ /F4 1 Tf /FontName /MSAM10 a;Sa.MAmIUdMHcmrH-Ghe$:4`42Ee$KR^ALZLs?! /F4 1 Tf /FontDescriptor 40 0 R /F4 1 Tf :KU1Mh0)`O;%)W,12NR+GZo'\rG0)I << 29.127 76.911 Td (1.1.) /FontDescriptor 40 0 R =HHTs?<0l3&4)AucOtoIWob=C(@6j\RD':d`$nX[5q8ZpT'+9k)a`'De%4ZS54D7h"R^"eJ(Y)t7HI LoU,_NUR9E2"D(:?60^&39iU]\'L^XfBC'>='L.3J56j)GOMUlYOI"]g#_l%96Q@q7-dmAY"D)^jW^ /F1 1 Tf A proposition is a sentence to which one and only one of the terms true or false can be meaningfully applied. /F1 1 Tf 11.96 0 0 11.96 0 0 Tm %^h!@Wq7dq?,\kiDs_^jR/&DZf/? Consider the statement "If a closed figure has four sides, then it is a square." 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