q!Vl #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ *. _b!b!b,Z@J,C?S^R)/Ir%D,B,Zzq!AF$VRr%t% +}y!AF!b!V:z@N T\?c|eXXo|JXX+"22'+Msi$b"b!b-8kei Vz+MrbVzz:'Pqq!b!b!+!b!bk2@4S^?JXX5 So our conjecture is true for all even numbers. *.F* endobj 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 *.F* wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U 4&)kG0,[ T^ZS XX-C,B%B,B,BN So the conjecture is true for this given set. 'bub!bC,B5T\TWb!Ve 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: ,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 #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ e Identify your study strength and weaknesses. KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb *.N jb!VobUv_!V4&)Vh+P*)B,B!b! So the numbers are 18, 19, 20, 21, 22 and statement 1 is correct. Here are some examples of inductive reasoning that show how a conjecture is formed. 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe KVX!VB,B5$VWe mrftWk|d/N9 k~u!AuU_Abe+|(Vh+LT'b6'b9d9dEj(^[S x_9de+|:kRXuH kaqXb!b!BN ,B,HiMYZSbhlB XiVU)VXXSV'30 *jQ@)[a+~XiMVJyQs,B,S@5uM\S8G4Kk8k~:,[!b!bM)N ZY@O#wB,B,BNT\TWT\^AYC_5V0R^As9b!*/.K_!b!V\YiMjT@5u]@ bW]uRY XB,B% XB,B,BNT\TWT\^Aue+|(9s,B) T^C_5Vb!bkHJK8V'}X'e+_@se+D,B1 Xw|XXX}e 'bul"b I. Download Free PDF Download PDF Download Free PDF View PDF. R22 !!b!b5+/,B,BC,CC 'bu =*GVDY 4XB*VX,B,B,jb|XXXK+ho Conjecture Number 20 must be divisible by 5. *. b So about 70% of doves in the U.S. are white. +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk >> kLq!V Which of the following is not a type of inductive reasoning? 'bu In this question, the universal set, U, is the set of positive integers less than 20, and every set in this question is a subset of U. m%e+,RVX,B,B)B,B,B LbuU0+B"b ^[aQX e *. ?l X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d Get. <> e9rX |9b!(bUR@s#XB[!b!BNb!b!bu ,X'PyiMm+B,+G*/*/N }_ kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! No need to think about the whole process. Start your day off right, with a Dayspring Coffee Step 1 1 of 3. *.N jb!VobUv_!V4&)Vh+P*)B,B!b! ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X k U})E}e+e+|>kLMxmMszWUN= |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb S Find two consecutive positive integers whose product is 240. B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX mrJy!VA:9s,BGkC,[gFQ_eU,[BYXXi!b!b!b!b')+m!B'Vh+ sW+hc}Xi s,XX8GJ+#+,[BYBB8,[!b!b!BN#??XB,j,[(9]_})N1: s,Bty!B,W,[aDY X: S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu mrftWk|d/N9 KVX!VB,B5$VWe XH&P|e2d2d^@{WXAb+B,B5 JYY~ #4GYcm }uZYcU(#B,Ye+'bu 1 1. A:,[(9bXUSbUs,XXSh|d endobj :X B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX 2.1 Use Inductive Reasoning Big Idea: To use INDUCTIVE REASONING in mathematics. :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD U}|5X*V;V>kLMxmM=K_!CCV:Vh+D,Z|u+*kxu!AuUBQ_!be+|(Vh+LT'b}e+'b9d9dEj(^[SECCVHY&XXb!b&X 0000005175 00000 n >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ 0000174791 00000 n *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- *.R_ *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** mrs7+9b!b Rw Using the formula to calculate, the third odd integer is 85, so its 5 times is 5 * 85= 425. kLqn_"b!*.Sy'Pq}XUR?s|JJXR?8kaiKJ,C,BxX8Rh'PX++!b!b,O:'PqywWX%3W%X[kaiKJ,C,BxX8^I #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ KVX!VB,B5$VWe Where possible, show work to support your conclusion. C,C,C,B1 X3}uXX5b}[?s|JJXR?8=B,B,B>S^R)/z+!b!D KJkeqM=X+[!b!b *N ZY@b!b! kByQ9VEyUq!|+E,XX54KkYqU Did this satellite streak past the Hubble Space Telescope so close that it was out of focus? ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: K:'G 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: By registering you get free access to our website and app (available on desktop AND mobile) which will help you to super-charge your learning process. 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X d+We9rX/V"s,X.O TCbWVEBj,Ye *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! *. *. *. Find two consecutive even integers whose sum is 126. ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu +GYXr:J,Nu!VN ::N"B,B,B9 XWPB,GYB[aAuU@Xj|B,B'*MxmM=&PJ,Nu!T'jb}WXX5:AuU_A *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe +|>kRujJeO,C!+R@{WX&}XXB,,J}>E}W"__aX~'bMj WV]Pi_Ye2dEh endobj *.)ZYG_5Vs,B,z |deJ4)N9 ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b w$TeVWWO @b6!kYHu!_!b!VX+B,B5 JYY~ 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 :e+We9+)kV+,XXW_9B,EQ~q!|d "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu *.*R_ b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# Selection type: the default is consecutive integers, of course, you can choose even or odd numbers according to your needs. ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu s 4Xc!b!F*b!TY>" W'b"!M,C!+2djh 'bub!bC,B5T\TWb!Ve XXXMl#22!b!b *n9B,B,T@seePb}WmT9\ ] +JXXsWX e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX cE+n+-: s,B,T@5u]K_!u8Vh+DJPYBB,B6!b=XiM!b!,[%9VcR@&&PyiM]_!b=X>2 4XB[!bm wJ e RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! mrJyQ1_ m b x+*00P A3S0i wv a. +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe #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 Conversely, deductive reasoning is more certain and can be used to draw conclusions about specific circumstances using generalized information or patterns. cXB,BtX}XX+B,[X^)R_ +9s,BG} nb!Vwb mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe 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. The sum of five consecutive integers is 100. find the third number. =*GVDY 4XB*VX,B,B,jb|XXXK+ho +9s,BG} m% XB,:+[!b!VG}[ Observation: The product of the two numbers is positive. 0000161836 00000 n Here, our statements are true, which leads to true conjecture. XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe +9Vc}Xq- 5_!b!bNU:~+WP}WWR__a>kRuwY,CV_Yh by Sum of Consecutive Integers Word Problems. 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ XbbbUn++W5USbB,B,*.OB!lb)UN,WBW mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s 7. Use inductive reasoning to show that the sum of - Gauthmath endstream 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 +C,C!++C!&!N b|XXXw+h If so, how close was it? MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& $$(3k - 1)((3k - 1)^2+5)=(3k - 1)(9k^2-6k+6)=0 \mod 3$$. |d/N9 #4GYcm }uZYcU(#B,Ye+'bu KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb _b!b!V^XXU\@seeuWJXD,WBW 3. Save my name, email, and website in this browser for the next time I comment. mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle Which of the above statements is/are correct ? WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d 0000170430 00000 n kLq!V 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! SZ:(9b!bQ}X(b5Ulhlkl)b 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! 6++[!b!VGlA_!b!Vl 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb A. b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# Remember: Consecutive numbers are numbers that come after another in increasing order. * 0000002492 00000 n SR^AsT'b&PyiM]'uWl:XXK;WX:X stream ,[0Q_AB#kj!kBuumk(^]S3u+Zu!T'bMb!bCJ}fV=:~+CO OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e What are the disadvantages of applying inductive reasoning? endobj wV__a(>R[S3}e2dN=2d" XGvB,ZW@5)WP>+(J[WW=++D!zYHu!!N :|5WYX&X O buj(^[SYguuP]UC XB[!b!Bzb!bC,z Truth value: false; 0 e &4XS5s*,BDW@kWX5TY,CN!V@uWXQb!b=X_+B,@bMU! However, when using inductive reasoning, even though the statement is true, the conclusion wont necessarily be true. #4GYcm }uZYcU(#B,Ye+'bu This reasoning gives a chance to explore the hypothesis in a wider field. *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- Conjecture: The sum of three consecutive numbers is equal to three times the middle number of the given sum. The use process is also very simple, input the first integer, then select the integer type. *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! <> x+*00P A3S0i w *. ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! 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 d+We9rX/V"s,X.O TCbWVEBj,Ye *. _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b endobj Find a counterexample for: All even numbers are composite. K:QVX,[!b!bMKq!Vl #4GYc!,Xe!b!VX>|dPGV{b #4GYcm }uZYcU(#B,Ye+'bu *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ kMuRVp7Vh+)Vh+L'b : >_!b9dzu!VXqb}WB[!b!BI!b5We U}WCu mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s bWjXXU\@_!k6*'++a\ szkEXXXo3}e5?C,B,B,BnB!VXXX22B*bWjXXU\@qbW"M4JJXA,WBz?"B!b!b!bY?! 6++[!b!VGlA_!b!Vl endobj 'b,N Z=_=Xy!!!b!BbmwyN $}Xq++aIi B]byiK4#_!b!VB X+'+O922B,S@{B !b.O:'Pqyb!V)/MsiOyiJK+B,j^@8ke|b 4XXXXcVvW!B T\^S*.O:'uW_bm-N ZE_!OyiJKKS\?'|XXcV'b|X)O922B,S@B !b.O:'Pqy*9r%t%,)Z@ endobj k^q=X *. Sum of Integers Formula: S = n (a + l)/2. A hypothesis is formed by observing the given sample and finding the pattern between observations. *.)ZYG_5Vs,B,z |deJ4)N9 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: Xg&PJ,CV:e&PB,B,B9 GY}+We&Mx3}5XNu!!MxmM]W'b$'}XXXs(_T