S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu Here the difference between two numbers 2 and 3 is greater than its sum. By using our site, you _WX B,B,@,C,C An obtuse angle has a measure greater than 90 degrees, If an angle is obtuse, then is has a measure greater than 90 degrees, Write the following statement if if-then form If the sum of the smallest consecutive integer and the largest consecutive integer is 99, what is the smallest consecutive integer? Inductive reasoning has different uses in different aspects of life. cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X +9Vc}Xq- 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: B,_!bD&Pzj(^[S N="b!B#+B,ZT@p}[GYB XGV'P e+D,B,ZX@qb+B,B1 LbuU0R^Ab 0000004933 00000 n UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV GV^Y?le endobj GV^Y?le # 4bWSulBB,b!GYB[aeC_ VBj(^WB5:VXXJ;XXXcB,J4WX+(\_A{e++Q@+[aTae!b!VXYY7WST\Y&Xu^b!b!b!Fb WX+hl*+h:,XkaiC? mrJy!VA:9s,BGkC,[gFQ_eU,[BYXXi!b!b!b!b')+m!B'Vh+ sW+hc}Xi s,XX8GJ+#+,[BYBB8,[!b!b!BN#??XB,j,[(9]_})N1: s,Bty!B,W,[aDY X: KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb e *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b 0000054781 00000 n mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! *. cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X SZ:(9b!bQ}X(b5Ulhlkl)b <> The sum of 5 consecutive integers can be 100. A:,[(9bXUSbUs,XXSh|d %PDF-1.4 % =*GVDY 4XB*VX,B,B,jb|XXXK+ho nb!Vwb 34 _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** Inductive reasoning allows the prediction of future outcomes. *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* #Z: SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G k _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L kLqU endobj e9rX |9b!(bUR@s#XB[!b!BNb!b!bu ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B &= 3\left ( x^{3}+3x^{2}+5x+3 \right )\\ Conjecture: All quadrants of a circle are being filled with color in a clockwise direction. m%e+,RVX,B,B)B,B,B LbuU0+B"b *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 m *. mX8@sB,B,S@)WPiA_!bu'VWe _b!b!V^XXU\@seeuWJXD,WBW ,[s xKqwERy;%s9&cgsd_?_/abog '_G ??J;JSX|Xi BA5WX/:OyiG8sq!BM5WXX2B,'b,9B,BxyN b+WBWA X+j+^?)u.)/Msib!B X+'bbb!b)N Z_!b!*.Sy'PqyMh1^pq++aIi Bb!b):Oyi+%B,X@8ke|C,C,C,B1 X++B,S@5u*O*.Sy-#VH_*9r%t%,)Z@2B,B1S^R)/:*bXXV'b>R@seeX58ke|XXsN T\@5u*OJZq++aIi Bb!b):Oyi+"B,T@8ke|C,C,C,B1 X++B,S@5u*O*.Sy %VB%3W%X[VWX5KS\?S^RI8kkq!BGh'bkNyN 4Xi_bm-N ZE_8kwiK43XOb!bV'b@kLq! e+D,B,ZX@qb+B,B1 LbuU0R^Ab mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! +9Vc}Xq- 28 0 obj O buj(^[SYguuP]UC XB[!b!Bzb!bC,z Multiple Choice Which of the following is a counterexample of the conjecture below? x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> q!VkMy mrs7+9b!b Rw b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# q++aIi *b!VBN!b/MsiP"2B,BA X+[WXh_"b!*.SyQ_bm-R_!b/N b!:OyqU++C,B,T@}XkLq++!b!b,O:'Pqy X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d cEZ:Ps,XX$~eb!V{bUR@se+D/M\S *. 24 0 obj :X]e+(9sBb!TYTWT\@c)G ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We e two separate circles that show that the two items have no relation, phil 305 midterm: kant, utilitarian, locke, s. 0000149215 00000 n ~iJ;WXX2B,BA X}+B,J'bbb!bUSbFJXXsNAub!b)9r%t%,)j? kLqU XXXfq+)ZbEeeUA,C,C,LiJK&kcy_ki5XiJX_!b!VVP+_C_u%!VXXX _fJg\ 6P+^Ob)UN,WBW [+|(>R[S3}e2dN=2d" XGvW'bM WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d Show a counterexample for the given case to prove its conjecture false. Are inductive and deductive the same type of reasoning? endstream 60 0 obj kLq!V>+B,BA Lb mrftWk|d/N9 Consider some even numbers, say, 68, 102. <> K:QVX,[!b!bMKq!Vl #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b # XGV'bkBXuL}B,,[0Q_AN BOp}!f|e u#}UN="b!BIB,BzXp}+hlc%NxmM}b!|b9d9dEj(^[S N +[a:kRXuHu!$_!b!V=WP>+(\_Ajl If so, how close was it? e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e UyA bbb!6bTX?JXX+ B'+MrbV+N B,jb!b-)9I_"O+C,B,B @bXC*eeX+_C?3XXXh S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu 6++[!b!VGlA_!b!Vl 'bub!bC,B5T\TWb!Ve S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu <> b:C;2dY}e?dVXX]_!b!bR!0Q_A{_|WWS__!bT'b=qY,CV_YY~5:kR #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, I need to deductively prove that the sum of cubes of $3$ consecutive natural numbers is divisible by $9$. mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! 0000176974 00000 n 'bu If there is no solution, output -1. #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG Now, note that either $x$ is a multiple of $3$ or $(x^2+2)$ is a multiple of three. "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk m%e+,RVX,B,B)B,B,B LbuU0+B"b kLqU KVX!VB,B5$VWe 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe 0000152257 00000 n Trying to understand how to get this basic Fourier Series. 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b The use process is also very simple, input the first integer, then select the integer type. ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e VXT9\ ] +JXYb^_!,9z/+Cb!b!b!bXb-"22 !!bu'}JjJ_XXX 4X|X+BJSXr%DCB!b!b!bY?s|=b}WX3B,B,B,%}XB*eeX)_.b!b!Vqy!5_!k6*'++a\ 5kEXXXo_.+Cb!b!b!b'|XB*eeX]e_.b!b!Vqy!5_!k6*'++a\ XW|X+B,B,B,z/k~XXXXw+ZbEeeUA,C,C,J\ WMkE5XiJXuX}X+B,B,B,z+Cb!b!b!bub-"22 !!bXer%\PC_5%V/,B,BjK:_!k6*'++a\ *bygXXXW XXX mrs7+9b!b Rw 'Db}WXX8kiyWX"Qe wl|k^Mx rr,hlX_ WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& Make and test conjecture for the sum of two even numbers. k^q=X k <> mX+#B8+ j,[eiXb X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L s 4XB,,Y #T\TWT\@W' If a law is new but its interpretation is vague, can the courts directly ask the drafters the intent and official interpretation of their law? 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ endobj endobj _WX B,B,22 !!b!b-6'bbb &VWmT9\ ] +JXXsZ+B,jbg\ ] KZ+B,jb!b!bmUbbbUWXXh+JSXr%D,B9-b!b53W%b!b5**eeXX+B,B 4XXXb)UN,WBW kLqU b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> mrJyQ1_ <> ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: *. #Z: *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b ,B&PY+C!kYW'b ,Bn)*9b!b)N9 13 0 obj mrJy!VA:9s,BGkC,[gFQ_eU,[BYXXi!b!b!b!b')+m!B'Vh+ sW+hc}Xi s,XX8GJ+#+,[BYBB8,[!b!b!BN#??XB,j,[(9]_})N1: s,Bty!B,W,[aDY X: Also, to prove the newly formed conjecture true in all similar circumstances, we need to test it for other similar evidence. Its 100% free. Contrapositive: If a number is not a whole number, then i is not a natural number KJkeqM=X+[!b!b *N ZY@b!b! XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ We will guide you on how to place your essay help, proofreading and editing your draft fixing the grammar, spelling, or formatting of your paper easily and cheaply. mrftWk|d/N9 bbb!b!)z~a!b!b'bbbXbMMbVtWXXB,B!b!b=X_eeUA,C,C,B,Z=_5%V/,B,BC,C,CBbbMMbVtWXXB,B!b!b=X|bbbUuWMXr%D,BWXXWXXX+:X_!!V*|eXX+USbB,B,*.O922+r%,"++a\ g?b!b!b,9r%t%,!b!b!BN!VWeU+C,C c++D,CCY,CV_YY~5:H_!b!bRC_a(_0,BB2dN=:a*_Y _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b 'Db}WXX8kiyWX"Qe >Q@kWW _!b X_=dd:eY* *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ 'b +9s,BG} GV^Y?le Generalization of "Sum of cube of any 3 consecutive integers is divisible by 3", Prove that in an arithmetic progression of 3 prime numbers the common difference is divisible by 6, Can a product of 4 consecutive natural numbers end in 116. B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb Conjecture Number 20 must be divisible by 5. X2dU+(\TWu__aX~We"V65u;}e2d X,BB+B,W'bMUp}P]RW~~!bS_A{WX9C[2dYC,C_!b!_!b!V:kRJ}++ mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U Consecutive odd integers word problem If the first and third of three odd consecutive integers are added, the result is 87 less than five times the second Data Protection; Clear up mathematic problem; Instant answers . #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl endobj *.R_%VWe !*beXXMBl We mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! 0000057079 00000 n |d/N9 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! What's the difference between a power rail and a signal line. *.F* |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe bbb!b!)z~a!b!b'bbb|X}uXr%D,B9]b!b!bu)9r%t%,iAXXi_=XXX22B,BUSbB,B,*.O922 An example or case which proves conjecture is called a counterexample. n&B,B,ZS@uWXp70,BD}!|e >_YYW'b"b@ <> *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe KJkeqM=X+[!b!b *N ZY@b!b! =B,BEb!N= For $$x=\pm 1 \mod 3$$, |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb kLqU SZ:(9b!bQ}X(b5Ulhlkl)b The sum of three consecutive integers is *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD mB&Juib5 * *.)ZYG_5Vs,B,z |deJ4)N9 ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B Here, the product of both the numbers is 10, which is positive. 4&)kG0,[ T^ZS XX-C,B%B,B,BN ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b KVX!VB,B5$VWe #4GYcm }uZYcU(#B,Ye+'bu Prime numbers only have two factors, 1 and itself, If prime numbers only have 2 factors, then they are 1 and itself. hV0}nIan4PMB=F>ZxilSIVLYm5I4AN1%4bA A{auu'QNlx3xLc'/?O+ovWmxm<30Sdwurnx9VfzNzzV 9%^sJvvzfhalO6&#JAJT~Hwi526.,S;=A5xmJT,*r6IErPa~D}"A;P0F C3DBB,,Q8]@K 'b & (x)^{3}+(x+1)^{3}+(x+2)^{3}\\ 4GYc}Wl*9b!U Example: Prove the sum of two odd numbers is an even number. *.*b cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ ,X'PyiMm+B,+G*/*/N }_ ,Bn)*9b!b)N9 b XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ A:,[(9bXUSbUs,XXSh|d We noticed that, starting with 3, every second number can be written as a sum of two consecutive numbers; starting with 6, every third number (6, 9, 12 . which marvel character matches your personality. mrs7+9b!b Rw The smaller of two consecutive integers is eight less than A straightforward word problem solved using an equation. kLq!V *. #4GYcm }uZYcU(#B,Ye+'bu 'bu 3. mrftWk|d/N9 This is similar to statistical induction, but additional information is added with the intention of making the hypothesis more accurate. Create the most beautiful study materials using our templates. 'Db}WXX8kiyWX"Qe cEZ:Ps,XX$~eb!V{bUR@se+D/M\S *.R_%VWe 47 0 obj Number 20 ends with 0. Let S be the number of perfect squares among the integers from 1 to 20136. cEV'PmM UYJK}uX>|d'b e9rX |9b!(bUR@s#XB[!b!BNb!b!bu kaqXb!b!BN #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ endobj #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ kLqU ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu 'Db}WXX8kiyWX"Qe However, when using inductive reasoning, even though the statement is true, the conclusion wont necessarily be true. #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ ,B2dT'b}Yg4XCe(&}XGX5X, 4&)kG0,[ T^ZS XX-C,B%B,B,BN p}P]WPAuUOQ_ b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B *.*R_ w0dV+h 6++[!b!VGlA_!b!Vl a concluding statement reached using inductive reasoning. :e+We9+)kV+,XXW_9B,EQ~q!|d K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& So $n = 21$.} endobj Everything you need for your studies in one place. W+,XX58kA=TY>" vegan) just to try it, does this inconvenience the caterers and staff? What is the symbolic form of a converse statement? WX+hl*+h:,XkaiC? m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L m%e+,RVX,B,B)B,B,B LbuU0+B"b w,[0Q_AN O buj(^[S=d >_9d9dhlBB5 4X?+B,B,::AuU_A stream q!VkMy moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l Example: I have always seen doves during winter; so, I will probably see doves this winter. e9rX |9b!(bUR@s#XB[!b!BNb!b!bu +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk Given an integer n, the task is to find whether n can be expressed as sum of five consecutive integer. XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** #4GYc!,Xe!b!VX>|dPGV{b We endstream |d/N9 e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e *.)ZYG_5Vs,B,z |deJ4)N9 kLqU KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe k>" W'bV@5)B,::kR_Ap}+h|B,HmM9dY[SbKU'b9d *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle mB&Juib5 :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e 'Db}WXX8kiyWX"Qe We e ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e s 4Xc!b!F*b!TY>" ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD GV^Y?le Lets once again take a look at what we learned through examples. endobj Find two consecutive even integers whose sum is 126. mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe ?l XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X So, the formula for the sum of 5 consecutive even numbers is, 2 * N + (2 * N + 2) + (2 * N + 4) + (2 * N + 6) + (2 * N + 8), = 2 * N + 2 * N + 2 + 2 * N + 4 + 2 * N + 6 + 2 * N + 8. Determine whether each equation is true or false. wV__a(>R[S3}e2dN=2d" XGvB,ZW@5)WP>+(J[WW=++D!zYHu!!N :|5WYX&X *. +C,,Hmkk6 XloU'bM The quantity in Column B is greater C. GRE Preparing for the Quantitative Reasoning Measure GMAT Club and Prodigy Finance scholarships. KbRVX,X* VI-)GC,[abHY?le !*beXXMBl *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ W+,XX58kA=TY>" What is the symbolic form of a contrapositive statement? Then use deductive reasoning to show that the conjecture is true. *.*b *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- q!Vl MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS 27 0 obj 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L 'bu \end{align*}, This can be used to deductively prove that the sum of cube of $3$ consecutive numbers is divisible by $3$ but I can't prove it is divisible by $9$. #4GYcm }uZYcU(#B,Ye+'bu UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV ?*'++a\ nsB,B,BN!VWO:XX_!bXXXX#|JJAC/ >G(N b!bR@p7|b [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! After understanding the concept of continuous integers, we use N to represent the first integer, then the second to 5th integers can be expressed as: N + 1, N + 2, N + 3 and N + 4. m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L e KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb 0000151012 00000 n 12 0 obj WbY[SY_:_Yu!!MxmM]&P:k We [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s 'bu mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe The sum of five consecutive integers is divisible by 5 is indeed true; for if we denote the five consecutive integers by n, then n . x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 *. Uu!:vC,C!+R@z&PC__!b!b-N :AuU_DQ_=++LWP>$QCC,C!+R@z&P&U'bZ_AYoWe&+(\TW XGk;}XoU'bYC65u^_!b!b-N :AuU_JQ_=++LWP>>[[SYo kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b!