83 0 obj <>/Filter/FlateDecode/ID[<7699FE2A76498BA3504AB9257FEAFED9>]/Index[77 17]/Info 76 0 R/Length 53/Prev 67195/Root 78 0 R/Size 94/Type/XRef/W[1 2 1]>>stream <> <> Contents PREFACE vii Part 1. �M�,� S)���r����� Solutions & Answers to Exercise Set 1 Giuseppe De Feo May 10, 2011 1 Equilibrium concepts Exercise 1 (Training and payment system, By Kim Swales) Two players: The employee (Raquel) and the employer (Vera). SYSTEMS OF LINEAR EQUATIONS3 1.1. �u�Q��y�V��|�_�G� ]x�P? The example is pretty simple where user needs to use the Set operators from SQL.Here user needs to use union set operator . Answers to Odd-Numbered Exercises8 Chapter 2. %PDF-1.4 Exercises Set 2 - Solutions.pdf - Set 2 1 Which of the following statements is NOT correct a If the market is weak form efficient we do not know whether. D�:���y���� vii. x�+͒�����f��6�9���xӈ���P�Z�ƶ��=v�fn!7��hQӯ���s(zZą�ÍF�4&����nVm� �6����6{|i�/���i-�ѸZ����6�Ŵ�J�,B�@K�� �'e5���o`����^#Zz�%C��V��B����"���o^W�ܲ��{i|Zy����d�A�x��R9'��]��tCM��sl����f���OϥPT�=]�Ǩyo%�^q���+ݳi�y�а�v�k�C浦�#�4�W �Z�L�H��י���xVv.�rš�����v��߉s�Y2��B`��gƧ��K��mn�������v�G�H��-n4�x���;���r��\��E�M��H"��)����)ֈ�8�g hޤV[o�0�+�q{`���H��UZ;Ԡu�! 93 0 obj <>stream Background 3 1.2. %%EOF In set theory this is done by declaring a universal set. ���Aih�^)w|�:��ޙ��Q���+=��R�����fW�p�sM>h������so Lk�D�����&�R��5s3+f�uܷe@�f�.� "������ \$)��\�K �( ��voqyQ��7a� t� �dc��]ݩI����(��I�����W@t���w�y���j�sP�^���AȒ�����P��Qo�8 �T(�,Z�@���Vb#���4 *I����ݴ�?��tPhpl4��+A�d�H Ҏ>G�P��ޑI�~^�A��ւ�kRI�#��K�H����4�ʃ a stand-alone book, since exercises and solutions are comprehensible independently of their source for likely readers. stream endstream endobj 78 0 obj <> endobj 79 0 obj <> endobj 80 0 obj <>stream SOLUTIONS * (1) Formal as a Tux and Informal as Jeans Describe the following sets in both formal and informal ways. �~�F��G�]�W�[��/�W���Lq+��;�b����9�ƱIq�>a+�=V�!�����.��!h�a�|ɟ-�UO^g�-�"A �~qZ!�/N���b��6 ��O�|S�଻��}3+�7�Ϩ.����rUq������9�%�G�;�Ίc}ӗ0��k��.3F���qg��N�c�:>��h����O"����[� �l��@��g�G���)�"�������x���ޒ�h��y�k-� ��^=�������ԝle�;��ڂ���ZX�Vي+�v��}��c�g���h�ݑT������a�vz�kD�y��?��0�. ARITHMETIC OF … Raquel has to choose whether to pursue training that costs \$1;000 to herself or not. 0 %�쏢 77 0 obj <> endobj �K� �%"���f�(��8,�V��C#*I:Fxs�}4bͲ ��N���� �i2%[�D6pi�%�% ���.�0'���!R��������"'\aN�qf��;�pN�c>9�DT\a�ꪝKvj����y+P݊�z��=���1��*"�K?m���m����J�JZ+{\$��y(��8Q�#z�!����;Qc��:��蕸�H�C�w%z!nU��{��_�^�k��=\$}X��V��:?�蕸�H�C�r]r�Dd9^�s+#�ev�� ��[�*U+�sQFx� i/�@��2�K�q�HFLC[n�C7�"�{�Џe�H��&8�c%u�� ݸ���܆�~,�C�.���w�!Q��ЏeTH��.t�. %äüöß O3|�J�p�;^I)C����,;g6��Jp��b��ſ]�RD{%��7Ӣ\=,g:~Czm��H�����G wA\$ Problems 7 1.4. %PDF-1.5 %���� h�bbd``b`�\$�C�`���@�+#��#1�Ɗ *� �G}a���4�0��hW��ѥVL������p )щԝ����6�axz��o��\�҇���ͩ��6�8�Ēxw���!G�X���b�ef�ww��Yk}~k�k���sC>mNs[�}��}^��+37qW����f-���4�/��]�Py���}�L��t��L��3�L�����yGy�o��v�ɸ�x�hM�@���;�7���o��D�G�k�N�G� To help readers not using this book together with Mathematical Statistics, lists of notation, terminology, and some probability distributions are given in the front of the book. 5 0 obj x��Ɏ,���_Qg��Z���� Ǘ< #�8N�I_��!�R�����3��ԈU�DqQQ5j����IM�S/09@������}��wӿ�C����������?M��a5}�y�A�B��QV9�U���ꢮ��>����TL��;����^�j��@|l��g@��k�� "\$�rK����:�HH��G{����s�.v�� This preview shows page 1 - 2 out of 4 pages. *�1��'(�[P^#�����b�;_[ �:��(�JGh}=������]B���yT�[�PA��E��\���R���sa�ǘg*�M��cw���.�"M޻O��6����'Q`MY�0�Z:D{CtE�����)Jm3l9�>[�D���z-�Zn��l���������3R���ٽ�c̿ g\� 2 0 obj H�[}K�`G���2/�m��S�ͶZȀ>q����y��>`�@1��)#��o�K9)�G#��,zI�mk#¹�+�Ȋ9B*�!�|͍�6���-�I���v���f":��k:�ON��r��j�du�������6Ѳ��� �h�/{�%? %PDF-1.4 hV���8�5�鄉6�@\$�Z�N����ž|��?��_elb�}�i BC]����.�2l ��� ����&̮8I�� . Exercises Set 2 - Solutions.pdf - Set 2 1 Which of the... School San Francisco State University; Course Title FINANCE FIN 351; Uploaded By DukeFinch475; Pages 4. MATRICES AND LINEAR EQUATIONS 1 Chapter 1. ~5[4!��ۣv���o�{F�[cH��Big�'V�D+̦ ��u���_�u�5,ԛp�11��B]]��9O��;U�ԝJ��/�7�K_Y�\$�uқtR)��TU���vsH�Y�P�-�!�O��W�L*�\$Ao>���?������fu@�C���'����,d�[�H5�Hk�� ���x�-� H���,����vm� �&l h�b```f``�d`b``Kg�e@ ^�3�Cr��N?_cN� � W���&����vn���W�}5���>�����������l��(���b E�l �B���f`x��Y���^F��^��cJ������4#w����Ϩ` <4� endstream endobj 81 0 obj <>stream If Ais a nite set having nelements, prove that Ahas exactly 2n distinct subsets. r��D�jtrFlZ(V*� ���ݓ�2�h�飭��q�.x%���~�H�S���ec#�&����� Tq��� ���R.�LYE��5�Xy�! =��ZSd��\�Q(����q�M�Dd��f:��yl�{���";%+"�"�c�V�&ǋH1��U�u��FM�3�S�p�)(2�d�OƠ8�Ԅ�߬\�y��c����J���9 r)��n:�ĚP���f�O'��u�HӚի�T�a� �3��ɚ2�2�1/���`%蟧�w'�)��I.#vF���wd��)�%��&Ȑa*����JN#vF����M*��L�t�\2\$dF��c��H�,=7s��,1AE�!��ʩ@Mf���F�(H�s3�5��"T� ֵ@Bn���F��u5���ʍP��aTNr3��4bgDA��k�%��MP���R�&��JN#vF��9j�P�F��Ŧ��Nr�qZ/�Ry *�jR�&��JN#vE�A.mG|��*WK)���i%��"b/f^�"7AE.C��jr��4bW���`��O �r�R !7�JN#vE���&Z�RAR !Z�&�3#���B�f���C? Exercises 4 1.3. – The empty set is denoted as or { }. We do know, however, that another new axiom will be needed here. ?m���A����� d",��Ҫ@�|�� [f�Ҳ�sJR�l5����C{�9�N�u後"T" ���u�� �?���s6�\$�,SE�H����붧����{�ǣ w�y0�}uy!QJ[�);�ߖmK~D�&=�����[ѿE_y����q�����>T � ܼc�E%�q���=:m�=��JA�� '��������Z2Q�NW���.M�B��=eJ�r�EgE�VR�џvi*@�l&�N��{�����G�X�2�*'�Ep��L���>)U�.�]ZR.��`\� o~��m�J��V #P6=�F;ޜ�oyi�j���e��� stream endstream endobj startxref Exercises and Problems in Linear Algebra John M. Erdman Portland State University Version July 13, 2014 c 2010 John M. Erdman E-mail address: erdman@pdx.edu. h��UM��6��W�Q* �_"��8�A}h-��E^[^k㵼��m~H�{3CR�� ����L��p�7�O����Z �5���@W'�Ǆ�-%� Set 2 1. �����Z�̕�Aǻ4�r,\���%�W@�/i�� ^��*�"&̤� � twenty-ﬁrst century will bring a solution. ��c�O1d8��#9F�8Q��ݐS]�ˏv �� vDt����C�E�Q�>6�l ���� Hb�4�v�I ͭ�6;�߮n� �w \$�C��C��T�d�@Y�o%��d��.;*#�E�����Z�7L���jc(��5��^'����P=xTy��xr����6�q�ǈ�Ҡ����0&8��]�h��a� L�SR攁�p�w]t:of!��ԙ�6����sbm�p���c��F�Gj��p�Hu� nrࡑ0���9+�nb�b���z\.F�Æ!��ZO2P��B�ě9�P8���/��JCr��jCn"wA}7(�OYД1��v���1`N��L��*��L1.Ekei�C��f_��. Although Elementary Set Theory is well-known and straightforward, the modern subject, Axiomatic Set Theory, is both conceptually more diﬃcult and more interesting. ܢ���t��l�\$MN��i�G��:�����(D��"�s��:�CG��?�|�ŗ�(ѳ��Cr�H/.HQL׹����aVm}\$ ����"۶i�\ }��>�}���P6��x8��cu+2K>�O! Deﬁnition 2.8 The universal set, at least for a given collection of set theoretic computations, is the set of all possible objects. x��]I�\�q������Щ��~�}��I�R�a[�D 0 `B �zg֚U��{B�B�~�Ւ�K�]�M^ �O���o�������'�����'����U���o�~} /�+%6画�~�\$,���r�o���͓?~s��]�5��_�r�*�xxq�ߴ�������A�HA{���\�>�n6���M�����?���?~�W*z�>��H����\$7gT>3A�4=|�u��/X�X�q��V�|W8��w8�t1���5����W�{^71���Id��e�W'k6�� ��WǓ��Tgp�f��8\,: – The universal set is denoted by U: the set of all objects under the consideration. �@���ӀX�0/���T4�ɓM�1�t���tӜ�9��kԕ�rQ�����iX.���e�k^/����ڢA2��i��ґ��x�N둮�2;T�nK�\$/z�5Y�Eoɜ7���DO��k�,�m!lՠim,Q���F��J�{rP�1���u�FI��������X�5���N?N|��t��fe�&�G_�?/����ѵHwQ:(e�Ӌ7kU���� �� ��8SJ?����M�� ��Y ��)�Q�h��>M���WU%qK�K0\$�~�3e��f�G�� =��Td�C�J�b�Ҁ)VHP�C.-�7S-�01�O7����ת��L:P� �%�",5�P��;0��,Ÿ0� If we declare our universal set to be the integers then {1 2, 2 3} is not a well deﬁned set because the objects used to deﬁne it are not members of the universal set. Myn�5��%����E\$Z��̭f�3D����6��x��O>��g}�d��K~P�*�O~����2f�Mv�t���ˇ�nHa���`8�r�*��bӚ�փk�H'�d��jzg�:���"HЬ �* �����w���o��cuޣ^��7�5s{���o_�� K�A7��� 5�1 FK_�\$D?��3C�F���e�8P�x���@�=�CؤF|�& All these statements will be discussed later in the book. ?,4���Z�z���|������\$ 'zQ `�MY�[�,ɪ�n����m[k����`�p