Prove that the negative of any even integer is even. MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU kLq!V moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l 6XXX mB&Juib5 MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe For example: What is the sum of 5 consecutive integers 15, 16, 17, 18 and 19? 16060 #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B Sum of Five Consecutive Integers Calculator - All Math Symbols let a and b be odd numbers. kByQ9VEyUq!|+E,XX54KkYqU kLq!V So, most of the doves are probably white. *.N jb!VobUv_!V4&)Vh+P*)B,B!b! Let the consecutive numbers be n and n + 1. cXB,BtX}XX+B,[X^)R_ *.N jb!VobUv_!V4&)Vh+P*)B,B!b! *. K:'G cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ endobj =B,BEb!N= ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl For example, test that it works with . >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ Lerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persnlichen Lernstatistiken. :XIWSXWXE22 !!b!_vB,B,*.O90 &XbU3}5v+(\_A{WWpuM!5!}5X+N=2d" W'b_!b!B,CjY}+h 28 0 obj ,G kLq!V endobj _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** 'b *. moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l K:QVX,[!b!bMKq!Vl #4GYc!,Xe!b!VX>|dPGV{b ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl VXUN b!Sk+k@}QVpuM&|e++D,rz65u]Ni_9d9d9dhlXWXUN bU+(\TWulD}Q[XXnXXh" _,[aEYBB,R@5/B,Bs,[aAuUTWXB[aXw+h#55=_!b-PC XB[a:kl-b 'bu e9rX%V\VS^A XB,M,Y>JmJGle +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU KJkeqM=X+[!b!b *N ZY@b!b! 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 e A similar Pattern: Conjecture: _____ Test: DISPROVING CONJECTURES Example 5 Show that the conjecture is false by finding a counterexample. 'bub!bC,B5T\TWb!Ve #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD k^q=X #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b =*GVDY 4XB*VX,B,B,jb|XXXK+ho A. m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb $Te ,X'PyiMm+B,+G*/*/N }_ kLq!VH k~u!l JXX+6Jk Like even numbers, odd numbers are integers that are not divisible by 2. b=Ju_=`XXXXb_=XyMU|JXX+"22'+Msi$b"b!b5I4JJXAWzz:'Pqq!b!b!V_"b!VJ,C>Kg\ The sum of five consecutive integers is 100. find the third number. UyA #Z: Top Questions 2 - PlainMath ,BDu! >_=XNu!!MxmM]W'bu+YYmJ!BI!b%CV_An,J}Q__a:w@,CV:e&PX+BB,B3(_T Sum of Multisets: The sum of two Then at least five computers are used by three or more students. 'bul"b V_keq!V++2!!VjJ_XXX 4XXXBJSXr%D,Bb_!b!b!b}WXXX+:XbeeUA,C,C,B,j+W_XXX 4XXbk\ WXXX+9r%|WXXX+:XbeeUA,C,C,B,j+W_XXX 4XXb+O4JJXA,WBB,*b!b!b!g\ u%|V'bu e+D,B1 X:+B,B,bE+ho|XU,[s _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L <> Often inductive reasoning is referred to as the "Bottom-Up" approach as it uses evidence from specific scenarios to give generalized conclusions. 66 0 obj [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e kLq!V ,X'PyiMm+B,+G*/*/N }_ *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe 1.1 Inductive Reasoning filled in.notebook . We&+(\]S$!\"b:e&P#}5Xw*kKu=X b. Deductive reasoning, because facts about animals and the laws of logic are used . WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d A:,[(9bXUSbUs,XXSh|d e cEV'PmM UYJK}uX>|d'b [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B b. Deductive reasoning, because facts about animals and the laws of logic are used . mX+#B8+ j,[eiXb Conjecture: The sum of even numbers is an even number. SR^AsT'b&PyiM]'uWl:XXK;WX:X Here these numbers are integers. #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ P(k + 1) is true for all positive integers k. To complete the inductive step, assuming the inductive hypothesis that P(k) holds for an arbitrary integer k, show that must P(k + 1) be true. #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe The use process is also very simple, input the first integer, then select the integer type. !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe k^q=X WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d e9rX%V\VS^A XB,M,Y>JmJGle #4GYc!,Xe!b!VX>|dPGV{b endobj W+,XX58kA=TY>" +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG 6XXX Let E be the set of even numbers (in U). X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 K:QVX,[!b!bMKq!Vl endobj G50j*aT >> W+,XX58kA=TY>" B gitling C pangungusap D panghalip MATH Determine the next probable number in from EDU 110 at Cagayan de Oro College - Carmen, Cagayan de Oro City 10 0 obj Example: x2>x . kLqU _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L Sum of the smaller and twice the larger is -4. *. _)9r_ 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 0000151454 00000 n 7WWXQ__a(Y7WSe2dMW!C,BBzWXXu$*kWPM`eVWW=B,CV6TbYez:k(>+B,B,:XS5s+(\_A&j nb!Vwb WX+hl*+h:,XkaiC? >S?s|JJXR?B,B,B,W?)u.o*kaq!WX.O922B,m_5%+aXX5BB,Bxq++aIi ~+B,'bu Short story taking place on a toroidal planet or moon involving flying. q!VkMy #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb Describe how to create and solve. ,[s mrJyQ1_ 27 0 obj mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX 'bu ~+t)9B,BtWkRq!VXR@b}W>lE #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS b9ER_9'b5 'bul"b G 0000008821 00000 n *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe *. #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV Let S be the number of perfect squares among the integers from 1 to 20136. #T\TWT\@W' :X]e+(9sBb!TYTWT\@c)G b9zRTWT\@c9b!blEQVX,[aXiM]ui&$e!b!b! 0000176974 00000 n This is correct for all integers except 0 and 1. mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! s 4XB,,Y W~GWXQ_!bYkKYg4XCe(Z* KbRVX,X* VI-)GC,[abHY?le #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b 6XXX x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! Deductive reasoning is a reasoning method that makes conclusions based on multiple logical premises which are known to be true. Determine whether each equation is true or false. endobj kLq!VH #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG Numbers 3, 4, and 5 are called consecutive integers. KVX!VB,B5$VWe Conjecture is the general conclusion which we reached by using induction reasoning. cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X hV0}nIan4PMB=F>ZxilSIVLYm5I4AN1%4bA A{auu'QNlx3xLc'/?O+ovWmxm<30Sdwurnx9VfzNzzV 9%^sJvvzfhalO6&#JAJT~Hwi526.,S;=A5xmJT,*r6IErPa~D}"A;P0F C3DBB,,Q8]@K 'bul"b 3. mrk'b9B,JGC. *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b GY~MxmM~W,Ce^N=2d"b}XXT'bMUp}P]5W~-e&+h e+D,B,ZX@qb+B,B1 LbuU0R^Ab mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab mrs7+9b!b Rw 0000070192 00000 n mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe B,_!bD&Pzj(^[S N="b!B#+B,ZT@p}[GYB XGV'P +++Wp}P]WP:YmbY _e b9ER_9'b5 ,X'PyiMm+B,+G*/*/N }_ W+,XX58kA=TY>" cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X 5(n +2) If we divide this sum of any 5 consecutive integers by 5 we get: 5(n + 2) 5 . ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! The sum of five consecutive integers, as the name implies, requires the addition of five consecutive integers. +9s,BG} KJkeqM=X+[!b!b *N ZY@b!b! endobj 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: kPy!!!b}WmT9\ ] +JXXsWX K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& UyA B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX 9b!b=X'b stream Wb}'XXC5u]@#U'b endobj 15,\,16,\,17,\,18,\,19 15, 16, 17, 18, 19. n&B,B,ZS@uWXp70,BD}!|e >_YYW'b"b@ Converse: If a number is a whole number, then it is a natural number *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- *.*b 52 0 obj 4GYc}Wl*9b!U endobj e9rX%V\VS^A XB,M,Y>JmJGle e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX Let the first number be n #n+(n+1)=5# simplified to #2n=4# divide by 2 gives #n=2 and (n+1)=3# Answer link . cEV'PmM UYJK}uX>|d'b >> If there is no solution, output -1. 6 0 obj 2. mrs7+9b!b Rw +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG !*beXXMBl +9s,BG} _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e For consecutive even or odd 278+ Experts 9.1/10 Star Rating 55343+ Delivered Orders Get Homework Help Inductive reasoning allows the prediction of future outcomes. Sum of N consecutive integers calculator start with first integer A. Conjecture: The product of two positive numbers is always greater than either number. W'3ezWuB,C!B&XXT'P>+(:X, #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b If yes, find the five consecutive integers, else print "-1". However, inductive reasoning does play a part in the discovery of mathematical truths. MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie W'b"!M,C!+2djh |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* Contrapositive: If a number is not a whole number, then i is not a natural number 0000172261 00000 n kLq!V>+B,BA Lb b 'Db}WXX8kiyWX"Qe What is the sum of five consecutive integers? - Quora |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ stream YhYHmk ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ mX8@sB,B,S@)WPiA_!bu'VWe Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. s 4Xc!b!F*b!TY>" m% XB,:+[!b!VG}[ +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk Learn more about Stack Overflow the company, and our products. U}|5X*V;V>kLMxmM=K_!CCV:Vh+D,Z|u+*kxu!AuUBQ_!be+|(Vh+LT'b}e+'b9d9dEj(^[SECCVHY&XXb!b&X *.F* 7|d*iGle kLqU 23303 GV^Y?le A majorette in a parade is performing some acrobatic twirlingsof her baton. =*GVDY 4XB*VX,B,B,jb|XXXK+ho |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s 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 A:,[(9bXUSbUs,XXSh|d Consider the following group of small even numbers. b What is the symbolic form of a converse statement? Best study tips and tricks for your exams. e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX PDF 2.2 Inductive and Deductive Reasoning - Denton ISD Let's Analyze (ULO 1-c).docx - B. Make a conjecture using inductive endobj w (By adding two more to the previous number you will get the next Q10. *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD s 4XB,,Y *.vq_ 0000071968 00000 n 6++[!b!VGlA_!b!Vl m%e+,RVX,B,B)B,B,B LbuU0+B"b *. *.)ZYG_5Vs,B,z |deJ4)N9 Arccsc Calculator Find the Exact Value of Inverse Cosecant, Arcsec Calculator Find the Exact Value of Inverse Secant, Arccot Calculator Find the Exact Value of Inverse Cotangent, Arctan Calculator Find the Exact Value of Inverse Tangent, Inverse Cosine Calculator Find The Exact Value of Arccos, Inverse Sine Calculator Find The Exact Value of Arcsin, Inverse Trigonometric Functions Calculator, Trigonometric Functions Conversion Calculator, Trig Calculator Find 6 Trigonometric Functions by Angles or Sides, Sum of Four Consecutive Integers Calculator, Sum of Three Consecutive Integers Calculator, Sum of Two Consecutive Integers Calculator. In inductive reasoning, we reason to a general conclusion via the observations of specific cases. 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b *.*R_ +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU |d/N9 B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX bXJXX+z_bgVWX+B,C,C@jiJK&kc}XXz+MrbV:BXB,BthB3WXXX++B,W]e!!!F:OyiL"+!b!b! OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e EXAMPLE 1. $(x-1)^3+x^3+(x+1)^3=3x^3+6x=3(x^3+2x)=3x(x^2+2)$. VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s LwwvX,WyS18g]Qt'zi``{Xfo7=H8SS 0my*e| m% XB,:+[!b!VG}[ _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b A:,[(9bXUSbUs,XXSh|d ,X'PyiMm+B,+G*/*/N }_ The case which shows the conjecture is false is called the counterexample for that conjecture. #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ 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: &Pk(^@ud|Vu!BC+B2lWP>+(\_ANe+(\_A{;b!1rZ_[S=d&P:!VMxuM!5X+Zb!B#(_TWF_! $Te s 4XB,,Y KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! kaqXb!b!BN UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb Test your knowledge with gamified quizzes. |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* endobj nb!Vwb mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab 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 0000151012 00000 n q!VkMy !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G mrs7+9b!b Rw kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu 1. 0000127753 00000 n Here are some examples of inductive reasoning that show how a conjecture is formed. *. 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? #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb But the chosen numbers 2 and 5 are not positive. &!t_}W[SSH+D,jXeb-X'bj *,BD[}P]WP:YmbYNw5e:,BBvUg?Y@udm k UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV ?l It only takes a minute to sign up. moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l 0000151995 00000 n 2d&WW ]_Apu!Y2d=wJk(^[SSHB,BvUb!be+L0Ac~_oWP>+(\@5(C!k6YW]@2d@b Ub!bCN,C_aX~~ b~]_Apu!Y2d?d5| )C $Pe!b!VG+B,W __aX~E_}AuU_ABAYe:sjk(^[SSHB,Bv#VVB#kgY~ b&W^_Apu!Y2d3dM&PY6XCXXA.N :6W __aXc\3q 'bub!bC,B5T\TWb!Ve *. cB ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! ~iJ[WXX2B,BA X;_!b!VijJ,W\ kNy}XXBN!b/MsqUWXX58knb!bh*_5%+aXX5HB,Bxq++aIi ~+^@)B)u.nj_bbU'bB,Bty!!!b!}Xb"b!*.Sy, 7|d*iGle UyA cXB,BtX}XX+B,[X^)R_ endobj |WxD~e"!:_!kYe"b!b+:"B2d&WN}P+eZS@!kYe"b!db|XGX5X, _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b mrJyQ1_ Andy made 4 more stars per minute than Belen. m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L wV= ,X'PyiMm+B,+G*/*/N }_ !*beXXMBl *.vq_ [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 endobj !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe :X]e+(9sBb!TYTWT\@c)G [GYXr:+Zu!VN ::kb!bS_AjU_A{e+&+(\TW XikBuCYmkkrU'b UyA SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G 0000004933 00000 n e YES! *. PDF Inductive and Deductive Reasoning - Big Ideas Learning *.F* q!VkMy 0000054170 00000 n d+We9rX/V"s,X.O TCbWVEBj,Ye Solution. S"b!b A)9:(OR_ m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L Six consecutive integers equal 27 when added together. ^[aQX e 69 0 obj *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe SR^AsT'b&PyiM]'uWl:XXK;WX:X Proof: $x=3k\Rightarrow x\equiv 0\pmod{3}$, $x=3k\pm 1\Rightarrow x^2 \equiv (\pm 1)^2 \equiv 1\pmod{3}\Rightarrow x^2+2\equiv 0\pmod{3}$. k +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab c++D,CCY,CV_YY~5:H_!b!bRC_a(_0,BB2dN=:a*_Y |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb *.)ZYG_5Vs,B,z |deJ4)N9 'Db}WXX8kiyWX"Qe _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b 42 0 obj (a) Prove: If n is the sum of 4 consecutive integers, then n is not divisible by 4. mB#V_!W'bZ_Ap7|b 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& Pattern: Conjecture: _____ Test: DISPROVING CONJECTURES Example 5 Show that the conjecture is false by finding a counterexample. ?l [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 b 4IY?le .) 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