e9rX%V\VS^A XB,M,Y>JmJGle #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl )_a:kY5!V@e+L(++B,7XS5s*,BD}VE}WN5+D,C!kxuY}e&&e endobj SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G 'Db}WXX8kiyWX"Qe ,!V!_!b=X+N=rFj(^]SOV"BIB,BshlD}e++Q@5&&P>u!k^N= kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu XXXMl#22!b!b *n9B,B,T@seePb}WmT9\ ] +JXXsWX You use inductive reasoning when you find a pattern in specific cases and then write a conjecture for the general case. s 4Xc!b!F*b!TY>" A. cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ <> 16060 OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e ,X'PyiMm+B,+G*/*/N }_ *.*R_ sum of five consecutive integers inductive reasoning 2022. . cEV'PmM UYJK}uX>|d'b #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ :e+We9+)kV+,XXW_9B,EQ~q!|d I need to deductively prove that the sum of cubes of $3$ consecutive natural numbers is divisible by $9$. 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 Inductive reasoning sequence example, Mouli Javia - StudySmarter Originals. 6XXX kaqXb!b!BN k^q=X 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b How do I find the angles of an isosceles triangle whose two base angles are equal and whose third angle is 10 less than three times a base angle? <> R22 !!b!b5+/,B,BC,CC_!xb)UN,WBW If the sum of the smallest consecutive integer and the largest consecutive integer is 99, what is the smallest consecutive integer? Then the numbers are x, x + 1, x + 2, x + 3, and x + 4. d+We9rX/V"s,X.O TCbWVEBj,Ye _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b |d/N9 62 0 obj cEV'PmM UYJK}uX>|d'b 49 0 obj [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e SZ:(9b!bQ}X(b5Ulhlkl)b $VRr%t% +abeXXMB,BthB3WXXX++B,W]e!!!bA)u.D,WBB,B-b!bI4JJXA,WB>XB,BthB3WXXX++B,W]e!!!V_b:OyiL"+!b!b! hW1mieHQ%Q"2nHpvWuGZdU$m(%ErF [96 6XXX 20 C. 12 D. 30 E. 56 16. . 9b!b=X'b *.*b The meaning of the questions: given n, n can be written in the form of at least two consecutive positive integers and the number of species. d+We9rX/V"s,X.O TCbWVEBj,Ye cB +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk 4&)kG0,[ T^ZS XX-C,B%B,B,BN XXXKXXXX ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! d+We9rX/V"s,X.O TCbWVEBj,Ye mX8@sB,B,S@)WPiA_!bu'VWe :e+We9+)kV+,XXW_9B,EQ~q!|d #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe ,BB:X+C!k~u!!MxuM!b!BI!VAuU_AdE,w+h Figure 4 Sum of Integers (Z). [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e I can prove deductively that they are divisible by $3$ but so far any combination I choose fails to prove the divisibility by $9$. wV__a(>R[S3}e2dN=2d" XGvB,ZW@5)WP>+(J[WW=++D!zYHu!!N :|5WYX&X endobj :e+We9+)kV+,XXW_9B,EQ~q!|d For example, test that it works with . mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU [++LBI $(+C!kYHu!_!b!G|XXB,,J}&E}W"__aX~'bMj WV]Ji_Ye2dEh JXX+6Jk <> Example: There are always white doves in the park. 2 0 obj Inductive reasoning, because a pattern is used to reach the conclusion. e mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe *.*R_ e9rX%V\VS^A XB,M,Y>JmJGle WP,[a(w,Bsj(L_!b}:!!+R@N Kj*TT'bY@B,B:*VXp}P]WPM`e Lets understand it by taking an example. 0000058664 00000 n ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ What sort of strategies would a medieval military use against a fantasy giant? SR^AsT'b&PyiM]'uWl:XXK;WX:X 1 5, 1 6, 1 7, 1 8, 1 9. 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 +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU 3. A:,[(9bXUSbUs,XXSh|d where a 1 - first term d is the common difference Types of Consecutive Integers Depending upon the type of integer, the different types of consecutive integers are as follows: Odd Consecutive Integers Even Consecutive Integers Positive Consecutive Integers kPy!!!b}WmT9\ ] +JXXsWX XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X ~+t)9B,BtWkRq!VXR@b}W>lE !b!V: kByQ9V8ke}uZYc!b=X&PyiM]&Py}#GVC,[!b!bi'bu ,X'PyiMm+B,+G*/*/N }_ *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV U'bY@uduS-b!b p}P]WPAuU_A/GYoc!bS@r+rr^@Mxu![ XB,BCS_Ap}:%VK=#5ufmM=WYb9d x+*00P A3S0ih ~ B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX +DHu!!k!@Y,CVBY~Xb!b!ez(p0+ *.N jb!VobUv_!V4&)Vh+P*)B,B!b! 'bu k^q=X Write the following statement in if-then form #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ endobj #4GYcm }uZYcU(#B,Ye+'bu +GY~W~~1e"!kMu!S;|e2d:~+D XWXXuWX=:Wx S sum of five consecutive integers inductive reasoning Isgho Votre ducation notre priorit 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe endstream ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl 35 0 obj 6Xb}kkq!~OyiJKKS\H2B,BA X+fN_!Gh'b *+b!V*.Sy'PqyMcW+WBWA X3OyiJKKS\K2B,BA X+ _!Gh'b5/+b!V*.Sy'PqyMW+WBWA X}OyiJKKS\N2B,BA X+zE_!Gh'b5kCXN T\@5u*R_!g\ ] KJ'bOyiJKKS\Q2B,BA X+tWC,C,C,B1 XMOCK_!z'PqyMT'_!Vkkq!Vb!bC,_R)/:7UkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6r%D,X*.Sy'PqyM+_bm-N +B,Xu4S^?)unkPq!B6BTy!!!b!B6I,WBB,S@5u*O*.S=}X+WBWA tbMXBN!b/MsiOyiJ[+C,B,T@8L4Iy!!!b!z,%+!b!b)O:'PqyBLq++aIi z"~8Qq!VKJ,C,BxX8F_ Is it suspicious or odd to stand by the gate of a GA airport watching the planes? mX8@sB,B,S@)WPiA_!bu'VWe endobj Then use deductive reasoning to show that the conjecture is true. Inductive Reasoning - PDFs. #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 I appreciate it, We've added a "Necessary cookies only" option to the cookie consent popup. *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb 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: mrk'b9B,JGC. sum of five consecutive integers inductive reasoning. +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe 0000053628 00000 n kLq++!b!b,O:'Pqy b9ER_9'b5 b 4IY?le >W@seeX5{jJ,W\ kNyk^i[22B,B X++B,\y!!!b!)\ #r%D,B9 T\^S*33W%X[+B,B,ByS^R)o'bs 4XXXXcr%'PqyMB,B_bmOyiJKJ,C,C,B,ZX@{B,B'bbb!b0B,WBB,S@5u*O. XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X kLq!V SR^AsT'b&PyiM]'uWl:XXK;WX:X 40 0 obj So if any one of the cases is false, the conjecture is considered false. ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ k^q=X *. stream ,X'PyiMm+B,+G*/*/N }_ mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G Suppose the sum of four consecutive odd integers is 184. *.F* #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ cXB,BtX}XX+B,[X^)R_ 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. WX+hl*+h:,XkaiC? *.R_ Inductive reasoning uses previous examples and patterns to form a conjecture. ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We KbRVX,X* VI-)GC,[abHY?le *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe '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 ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We *.F* 10 0 obj b"b=XQ_!b!b!b}pV'bujB*eeXXM|uXXXhZB%JSXr%D,J4KXg\ WJ|eXX8S6bu !!VK4 e XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X kLq!V>+B,BA Lb OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e 'Db}WXX8kiyWX"Qe :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG >> k b *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe a. Then use deductive reasoning to show that the conjecture is true. b. Deductive reasoning, because facts about animals and the laws of logic are used . *. 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ The sum of two consecutive odd integers is 44. YES! You have then the sum of three consecutive cubes is ( x 1) 3 + x 3 + ( x + 1) 3 = 3 x 3 + 6 x = 3 x ( x 2 + 2). X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s $(x-1)^3+x^3+(x+1)^3=3x^3+6x=3(x^3+2x)=3x(x^2+2)$. m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L two separate circles that show that the two items have no relation, phil 305 midterm: kant, utilitarian, locke, s. 'bub!bC,B5T\TWb!Ve Using the formula to calculate, the third integer is 17, so its 5 times is 5 * 17 = 85. e9rX%V\VS^A XB,M,Y>JmJGle K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& So, the given conjecture is false. 0000057583 00000 n .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ K:'G 'bu junho 16, 2022. mrk'b9B,JGC. ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu Hence, it is an even number, as it is a multiple of 2 and m+n is an integer. WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d *. b mB&Juib5 ,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 ,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 +|>kRujJeO,C!+R@{WX&}XXB,,J}>E}W"__aX~'bMj WV]Pi_Ye2dEh 16060 XA 2, 2 XB} 1 2}, 2 XC 3, 10 XD 2, 21 23. 7|d*iGle q++aIi #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 ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu endobj 'bu #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX '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 :X]e+(9sBb!TYTWT\@c)G _WX B,B,@,C,C A conjecture is said to be true if it is true for all the cases and observations. 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ m% XB,:+[!b!VG}[ Formula for sum of 'n' terms of an arithmetic sequence: S n = n 2 [ 2 a 1 + ( n - 1) d]. ,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 _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L Be perfectly prepared on time with an individual plan. kByQ9VEyUq!|+E,XX54KkYqU November 2, 2021 . *.)ZYG_5Vs,B,z |deJ4)N9 MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ R22 !!b!b5+/,B,BC,CC{BJSXr%D,Bb_!b!b!b}pV'buj-n *.)ZYG_5Vs,B,z |deJ4)N9 #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ If so, how close was it? cEV'PmM UYJK}uX>|d'b 6++[!b!VGlA_!b!Vl :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e endobj endobj :X]e+(9sBb!TYTWT\@c)G #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ "l!O)|jn17,JwO@$ p,z(f`D0UH i4#6a #7n4f2 E$"94%8~\Ygtp9Y>qhtj8grgb{FjxAaQ{n=Gko +lHb. wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U #4GYc!,Xe!b!VX>|dPGV{b trailer << /Size 310 /Info 201 0 R /Root 204 0 R /Prev 480387 /ID[<3cd60dd519d6ab5c5d219b7bb7f06c6b><49b31575350be81b6df4257ea55a4316>] >> startxref 0 %%EOF 204 0 obj << /Type /Catalog /Pages 200 0 R /Metadata 202 0 R /AcroForm 206 0 R /Outlines 196 0 R /Names 207 0 R /OpenAction 205 0 R /ViewerPreferences << /HideToolbar true /HideMenubar true >> >> endobj 205 0 obj << /S /GoTo /D [ 210 0 R /FitH -32768 ] >> endobj 206 0 obj << /Fields [ 221 0 R 222 0 R 223 0 R 224 0 R 225 0 R 226 0 R 227 0 R 231 0 R 232 0 R 199 0 R 97 0 R 99 0 R 101 0 R 103 0 R 105 0 R 107 0 R 109 0 R 111 0 R 113 0 R 116 0 R 118 0 R 120 0 R 122 0 R 124 0 R 126 0 R 128 0 R 130 0 R 132 0 R 135 0 R 137 0 R 139 0 R 141 0 R 143 0 R 145 0 R 147 0 R 149 0 R 151 0 R 154 0 R 156 0 R 158 0 R 160 0 R 162 0 R 164 0 R 166 0 R 168 0 R 170 0 R 178 0 R 180 0 R 182 0 R 184 0 R 186 0 R 188 0 R 190 0 R 192 0 R 194 0 R 198 0 R ] /DR << /Font << /ZaDb 197 0 R /Helv 229 0 R >> /Encoding << /PDFDocEncoding 230 0 R >> >> /DA (/Helv 0 Tf 0 g ) >> endobj 207 0 obj << /JavaScript 208 0 R >> endobj 208 0 obj << /Names [ (disclosed)209 0 R ] >> endobj 209 0 obj << /S /JavaScript /JS (this.disclosed = true;\r\n) >> endobj 308 0 obj << /S 957 /O 1549 /V 1565 /Filter /FlateDecode /Length 309 0 R >> stream For example, if you leave for work and it's raining outside, you reasonably assume that it will rain the whole way and decide to carry an umbrella. 35 *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- 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: +9_aX~~ bS@5:_Yu}e2d'!N=+D,k@XuWXO <> 0000167617 00000 n MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B 6++[!b!VGlA_!b!Vl mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb Example 2: The sum of an odd and an even number If an odd number and an even number are added, will the sum be an odd or an even number? S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu #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 cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX This is opposed to a deductive reasoning Deductive Reasoning is the process of reasoning to a specific conclusion from a series of general statements. b 4IY?le q!Vl making a conclusion based on observations or patterns, a concluding statement reached using inductive reasoning, conjecture: double the previous term and add 1, conjecture: each term is a square; to find the next term, square it, An example that proves a conjecture is false, Determine whether the conjecture is true or false. Answer (1 of 7): What you wrote is false. endstream 7|d*iGle *. 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 SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G #T\TWT\@W' <> N=2d" Yu!_!b!b-N :AuU_MQ_=++LWP>>[[S In this question, the universal set, U, is the set of positive integers less than 20, and every set in this question is a subset of U. K:QVX,[!b!bMKq!Vl Are inductive and deductive the same type of reasoning? Step 3 Test your conjecture using other numbers. GV^Y?le cEV'PmM UYJK}uX>|d'b +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk