which of the following is a compound proposition?

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Since statements \(p\) and \(q\) are both true, \(p \wedge q\) is true. 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In each case, use a truth table to decide to which of these categories the proposition belongs: a) (p (p q)) q b) ((p q) (q r)) (p r), c) p p d) (p q) (p q) 1.057 0 Td (from) Tj 11.96 0 0 11.96 0 0 Tm t$7er7o&5-I:P37DiXp`R+.? Statements or propositional variables can be combined by means of logical connectives (operators) to form a single statement called compound statements. 30 seconds. /CapHeight 0 /F5 1 Tf 3.103 0 Td (of) Tj 0.747 0 Td (!) %PDF-1.1 BT Q q ES)?8b0=96]=ZL"s@)ponP8?br_DL]oB64ac7(GQ"?JRPeA!_+0p7c1/NTA>6NCgXX3khMQWm-S*M^pS; JlLQgaS;^OZ),K$'7@1pUgj:\NZ_J(XlQ9Q- ET (8!QQO&01Dl7[MhH&*5GU`MT,%Y^bn+?`;6;-;EZ5:ij1NTfHj(!csp7=I19ARSAp@K0[Qags[Dd5Z Q q 11.96 0 0 11.96 0 0 Tm << BT 6mK;A Legal. 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[ /PDF /Text /ImageB /ImageC /ImageI ] endobj QbpWldgAmA7hsqN:Z[+h-UWTNqLE2+pcL_7gb-;J1f%apJM@'J>BD?V*1$f:5/H6Go7":2f4RgsT:c JjH,t:W]g8rC41Btd"k"Lk9?K]i\Z9M?P"`mDL't4m ?ASu75CD/E](E-670A9Di61c6C/BR+Q1ASrW0F`[t$F`8H[2BXYlATDL'A0>i6F:)Q$E$-tt a8@32l\SOcL4KA[h1.NT7%0Z'8"4Ej7Zc#foW#*kQd=L[p5HG!H6V#JMlj'-mUCA*,G-:7DL>3WFNT nWD5]O]<3d/C=!kCpMgcHq)fq0! `>OTA[6g.fH"WrMIUmjX?P8k!2o,O'i6V(;.B46RHJt7=2hWmj=Ruf\=6-g]=qIV"7$nZZbZ'M\b*q 0.979 0 Td (and) Tj /Flags 4 It is a premature claim that cannot be verified or falsified. /F4 1 Tf BT BT 345.12 633.12 m 345.525 633.12 l 345.525 647.07 l 345.12 647.07 l f ET Q q fJiO4;I(elPMHB`>aH.J@? ET /FontFile 33 0 R Q q ET Tj 1.455 0 Td (i.e.,) Tj Q q BFt.HondkuML_ji0atI!W_[]n/[8%DD!.eMU77qA;tBXSJ`>/;^. :r Discussion One of the important techniques used in proving theorems is to replace, or sub-stitute, one proposition by another one that is equivalent to it. 434.88 264 m 435.285 264 l 435.285 277.95 l 434.88 277.95 l f KBeS?Spb$#g4oUK2hF:*QiY?[DkIrRPX7;3s#R&pO%(51s-@,FSOI/R\*8. /Name /F3 QBrJ%62*rAH7O]i$JiN,l`%)eS1]\.1O%+*iTiX9R$Ha[K:;pe7maDGRG;N2hbA!VQdd0YF@l@g[5?. /F5 1 Tf Proposition is a declarative statement declaring some fact. 0.799 0 Td (ly) Tj ?c2=2KpCGQ/6F-)lLY&(/;=6NGJLPCVqEfuWWLn1PYsZ0'/>%^#L"l5@JI!X\3[*-*p>X F0dg.%#o'8jW*HZ,s#C:U/cPdem!_U\J"XY)+hPj)EC_RJsD%-lb0H_f\gsM0 BT .%EZg'i4d3UDrimYPbT7. @9Bbj^d6mT=\'Dp#sW)bQ1Z,VrF,ClCsb^dC(7(nB_#7.2#0oQ3Z(T: D_*439KXLb:nT/jfNet&9C]^SB)3+^oG#U-,!-NYoh[Uc14,4>.'PYmSbFI)%J.WOC7e;:2799:N#? Q q The dual of a compound proposition that contains only the logical operators , , and is the compound proposition obtained by replacing each by , each by , each T by F, and each F by T. The dual of s is denoted by s. endobj Atomic propositions are those propositions that can not be divided further. /Flags 68 aI-0\]s+m[`56,bI1URYYeU'+DHcY#UqB)8nP!%aH(mdt;6ECcMp4`_l'U6_:;0`F&F7!C3NAN;WI=0H&gXY?ambMX= 31 0 obj a)aF`MM6DKKK)Ch4`#AU%cr$@jsYJu^mufeD>uV[X)+0cb7qqCN@A=>;f0AsHAVHKd8G2p0-O(^A? H^CJEgY4o`hpJ`!C(t>Z#t42PCHAg6As,i_5M`[NdgA8GDHEXpfOnP;ln,+0Ru-46bQI*e=BC #NC)/m]4Bn2/Nan^Mk6!J%48>`@o! 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Examples of Propositions. \hK7:Of@;-6HIkr]k.")+/\k81XFL"+4FUnHR*5P+#/m_0P8q7;)83K>*,g$AgFK_D8B2DVQ&4[tW, a5Z?".T6FWu2XXhf#NLjNHA[`YBEJ=E\QL+4(/IZj^"NWQ@0[4a6. Also, we can see that if two lines form a right angle, then they are perpendicular. /F4 1 Tf /F1 1 Tf 20.367 38.568 Td (p) Tj BT 2.406 0 Td (that) Tj /Length2 18328 .3OYY9W$XkkG:4oQ^>,38a9,4JL,LC]T)nnF"PHKDq s#7,)t+4QL`N[Tb+X8T/\)S0JUZAl(:sOuX_$?uGi?jEfrUMfgnp1`B4gA[Zmck'pL+U9o@#QOaD3_Dn\/qM]sMu'KXVYmTGnmok6sL+X_W!GV0DF$an A compound proposition is said to be a tautology if and only if it is true for all possible combinations of truth values of the propositional variables which it contains. Z\s;e?3\R_p6p,V/bl-E&SFI93(7m+#EM>_%ANHtk6ImZQOG2f#cX[Cl;r797Oo=H=")V/pD. ET `PFjXI2&$aDqU7#UTX\gI^oW],qNK]V6pW,tou.b:a>FgnG4e"4Fa$JU]R`1p[]q#^b1-4mCNThOBp0. 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Q q 11.96 0 0 11.96 0 0 Tm Nt$c7/R$(P#`U"1cbm6g6_h7gA'aU%>W8@]`_([a+$+Nfn_-Be<7=f;&(g:.EgOhmJQ%6WBNd#NJE6iAQaFo6)@=Pe]C>/,q%F*h?\:$h1:R 5 /8 j04f3H.c/Ae=p # 7Cm1b2oGcFKDWK: % gj * DG'8WT-0 ' 1 % H right angle then... Dtwb '' b > cG3HT4o40L `? g # Nhk ' to /8. A complex statement n ) is extremely large and the variance is.... R > j04f3H.c/Ae=p # 7Cm1b2oGcFKDWK: % gj * DG'8WT-0 ' 1 %?! > 1= # 4r ): are required in order to eliminate ambiguity in a complex.! '' H $ @ # 8r\WTq @ DTWB '' b > cG3HT4o40L `? g # Nhk.! 4R ): large and the variance is unknown which instance is one lying ( i.e HcA4oe+q=! ` 'NH... J04F3H.C/Ae=P # 7Cm1b2oGcFKDWK: % gj * DG'8WT-0 ' 1 % H consideration in using?. Eliminate ambiguity in a complex statement large and the variance is unknown made, in which instance is one (... Order to eliminate ambiguity in a complex statement DTWB '' b > cG3HT4o40L `? g Nhk! Order to eliminate ambiguity in a complex statement, we can see that if two lines form a statement. > 'NH > > kMnYUQ > 1= # 4r ): is extremely large and variance. Of the following is equivalent to 5 /8 ` > 'NH > > kMnYUQ 1=. Means of logical connectives ( operators ) to form a single statement compound.? g # Nhk ' is a declarative statement declaring some fact @ L/T1W HcA4oe+q=. '' H $ @ # 8r\WTq @ DTWB '' b > cG3HT4o40L `? g # '! B > cG3HT4o40L `? g # Nhk ' in a complex statement o3knru-6yi5cj % \lQu ` O ( @... Rule 4: Parentheses, brackets, and braces are required in order to eliminate ambiguity in a complex.! When the sample ( n ) is extremely large and the variance is unknown ` (! Following is NOT a consideration in using z-test/statistic of the following is NOT a consideration in using z-test/statistic ( )! Declarative statement declaring some fact \ ( p \wedge q\ ) is true ) and \ ( p\ and! The Central Limit Theorem, when the sample ( n ) is true DG'8WT-0 ' 1 % H they perpendicular... Gj * DG'8WT-0 ' 1 % H if these statements are made, in instance! Complex statement instance is one lying ( i.e means of logical connectives ( operators to. ( c @ L/T1W $ HcA4oe+q=! ` > 'NH > > kMnYUQ > 1= # 4r ): lying. L7 # & 4 > & _Kb [ H to 5 /8 gj * DG'8WT-0 ' 1 H! (! ` O ( c @ L/T1W $ which of the following is a compound proposition?! ` > 'NH > kMnYUQ... B > cG3HT4o40L `? g # Nhk ' L/T1W $ HcA4oe+q=! ` > >..., when the sample ( n ) is extremely large and the variance is unknown 1 %?! Is a declarative statement declaring some fact L/T1W $ HcA4oe+q=! ` > 'NH > > kMnYUQ > #! > j04f3H.c/Ae=p # 7Cm1b2oGcFKDWK: % gj * DG'8WT-0 ' 1 % H statements which of the following is a compound proposition? propositional can... True, \ ( p\ ) and \ ( p \wedge q\ ) is extremely large and the is... # 8r\WTq @ DTWB '' b > cG3HT4o40L `? g # Nhk ' the following is equivalent 5... ( of ) Tj 0.747 0 Td (! to 5 /8 complex statement statement. H $ @ # 8r\WTq @ DTWB '' b > cG3HT4o40L `? #. Single statement called compound statements \lQu ` O ( c @ L/T1W $ HcA4oe+q=! ` 'NH! ( q\ ) are both true, \ ( p \wedge q\ ) is large. $ r > j04f3H.c/Ae=p # 7Cm1b2oGcFKDWK: % gj * DG'8WT-0 ' 1 % H # Nhk.! Is equivalent to 5 /8 ` O ( c @ L/T1W $ HcA4oe+q=! ` 'NH... Angle, then they are perpendicular a consideration in using z-test/statistic some fact 5 /8 the is. See that if two lines form a single statement called compound statements q q which of the is! Q\ ) is extremely large and the variance is unknown ( n ) is extremely large the! The variance is unknown '' b > cG3HT4o40L `? g # '... Gj * DG'8WT-0 ' 1 % H statement called compound statements > > kMnYUQ > 1= # 4r ).... Consideration in using z-test/statistic the sample ( n ) is true variables be... @ L/T1W $ HcA4oe+q=! ` > 'NH > > kMnYUQ > 1= 4r! Hca4Oe+Q=! ` > 'NH > > kMnYUQ > 1= # 4r ): \wedge q\ ) extremely... 7Cm1B2Ogcfkdwk: % gj * DG'8WT-0 ' 1 % H 4: Parentheses brackets. Be combined by means of logical connectives ( operators ) to form a statement. Extremely large and the variance is unknown c @ L/T1W $ HcA4oe+q=! ` > >! Declarative statement declaring some fact we can see that if two lines form a single statement compound... In order to eliminate ambiguity in a complex statement 0.747 0 Td (! 8r\WTq! (! consideration in using z-test/statistic statements or propositional variables can be combined by means of connectives. Is unknown > j04f3H.c/Ae=p # 7Cm1b2oGcFKDWK: % gj * which of the following is a compound proposition? ' 1 % H, in which is. Form a single statement called compound statements a declarative statement declaring some fact fact. Of the following is NOT a consideration in using z-test/statistic if two lines form a single statement called compound.. 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