Notions of implication, converse, inverse, contrapositive, negation, and contradiction. Discrete structures are foundational material for computer science. 21:59 No comments: Definition : Sets. Explain with examples the basic terminology of functions, relations, and sets. 6 0 obj >> Apply formal methods of symbolic propositional and predicate logic. ���t���L���:_f�����Mlx�?��"�A�R�H�$h(+�23nk��dmO) �ƶ���B3�i�Ь��p;`�4 �qg;�0t��0���Ц/.���1U��mR�����s�G|��W$�q�BI�����]cs�|L�Z0�����l�(�yw��QeȀ�_!�Ls@!$�%��mH^q�Mo�OR�����r�LKb�8��A���Q�z�W?�m�Oendstream << /Type /Page /Parent 3 0 R /Resources 6 0 R /Contents 4 0 R >> Copyright © 2008, ACM, Inc. and IEEE, Inc. SIGCSE Committee Report On the Implementation of a Discrete Mathematics Course, http://wiki.acm.org/cs2001/index.php?title=Discrete_structures, To give feedback on this area of revision, go to, Functions (surjections, injections, inverses, composition), Relations (reflexivity, symmetry, transitivity, equivalence relations), Sets (Venn diagrams, complements, Cartesian products, power sets). Describe how formal tools of symbolic logic are used to model real-life situations, including those arising in computing contexts such as program correctness, database queries, and algorithms. Discrete structures include important material from such areas as set theory, logic, graph theory, and combinatorics. 5 0 obj Relate graphs and trees to data structures, algorithms, and counting. We have gathered together here a body of material of a mathematical nature that computer science education must include, and that computer science educators know well enough to specify in great detail. Multiple choice questions on Discrete Structures for UGC NET Computer science. x� ��8��{O���S�����d�1Cwʬc�2v�rXn����g���D`"0�L&���D`"0�L&���D`"0�L&���D`"0�L&���D��D�����;��TgV���# ���߿�������}v���$9^8��D`"����z. e!��ཎ÷�D���(j�r6���OL��9x3�K�I�$=������A��a72d�B���R�K� Perform the operations associated with sets, functions, and relations. [ 0 1 ] /Extend [ false false ] /Function 17 0 R >> Demonstrate basic counting principles, including uses of diagonalization and the pigeonhole principle. >> endobj << /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] /ColorSpace << /Cs1 8 0 R A set is said to contain its elements. %PDF-1.4 Normal forms (conjunctive and disjunctive). Wordpress Insert Record Into Table And Get Last Insert Id, 2013 December UGC NET Previous Years Solved Paper I, Dynamic Memory Allocation and Dynamic Structures, 2013 September UGC NET Previous Years Solved Paper I, 2013 June UGC NET Previous Years Solved Paper I. << /Length 11 0 R /Type /XObject /Subtype /Image /Width 393 /Height 64 /Interpolate x�UKo�0��W��%9��+�ÉGq 6�a [�K�݂Ŀ��IܖnˮǓ��7��)���F��w�E�S���'�I'/����?��篻Yo�o⦍��[:���4�dhU��Ű� D�8���� Describe the importance and limitations of predicate logic. endobj It is increasingly being applied in the practical fields of mathematics and computer science. Model problems in computer science using graphs and trees. HK��_,��Z�^s�IW���Q~�XޥvCe �u-P7w�r?�{��(�x� Outline the basic structure of and give examples of each proof technique described in this unit. For example, an ability to create and understand a proof—either a formal symbolic proof or a less formal but still mathematically rigorous argument—is essential in formal specification, in verification, in databases, and in cryptography. >> /Font << /TT4 15 0 R /TT2 13 0 R /TT3 14 0 R /TT1 12 0 R >> /XObject << *���r����G����&��A��$�Ť���S;�v�-b4���,�p،��?��^fjg ��E���� Ρ��m��ݑ�ȝV�Ş�����d>��$��I�D�6���8��f����Co�Z[DG����M����"����E�I�yD>�M/����x�>*C�)�ݣ��3C�L~�ԑ��yd: A function from Ato B is an association to each element in Aof exactly one element in B. Graph theory concepts are used in networks, operating systems, and compilers. >> Unknown . 948 The objects in a set are called the elements, or members,of the set. Discrete Structures; Sets in Discrete Structures; Friday, 18 July 2014. �v�6�0|J�e�@Y��I8d�N�@��pJ�mЬc��BQG Q���i:�Ȁ'���b�9v��.��F:۹@�n��!�C$H{1�q�N�1��e�@�3�L����U�q�M|^�TM�*��ү�,Uc�My�@5�Wg59�.җ$zY���E��J:^:�|��-�b�nn� C:�#������S�)�)�M-�x
���i� ����X}�c�P����f^$����'�oZ��X@W^�p��`��T��Ľ��}-���%�8`��\`�Q�s,��>ۢt3{���#W����� �h�T=�c00��i���)��? Finally, we note that while areas often have somewhat fuzzy boundaries, this is especially true for discrete structures. This page has been accessed 49,051 times. endobj /Resources 1 0 R /ProcSet [ /PDF /Text ] Infinite Sets George Voutsadakis (LSSU) Discrete Structures for Computer Science August 2018 2 / 66. In particular, this class is meant to introduce logic, proofs, sets, relations, functions, counting, and probability, with an emphasis on applications in computer science. Toggle navigation. The material in discrete structures is pervasive in the areas of data structures and algorithms but appears elsewhere in computer science as well. However, the decision about where to draw the line between this area and the Algorithms and Complexity area (AL) on the one hand, and topics left only as supporting mathematics on the other hand, was inevitably somewhat arbitrary. Apply the binomial theorem to independent events and Bayes’ theorem to dependent events. 4 0 obj Here you can access and discuss Multiple choice questions and answers for various compitative exams and interviews. Practice these MCQ questions and answers for UGC NET computer science preparation. endobj 2 0 obj /Length 647 ?�=����u�ˠ��[�M`���#�i��L�c0��4�L�dsVԤGluj /Im1 10 0 R >> /Shading << /Sh1 9 0 R >> >> endobj << /Length 5 0 R /Filter /FlateDecode >> The material in discrete mathematics is pervasive in the areas of data structures and algorithms but appears elsewhere in computer science as well. Discrete Structures (DS) Discrete structures are foundational material for computer science. /Length 352 %PDF-1.3 stream h��O�!%7. Discrete Structures for Computer Science George Voutsadakis1 1Mathematics and Computer Science Lake Superior State University ... Let Aand B be sets. Demonstrate different traversal methods for trees and graphs. true /ColorSpace 8 0 R /SMask 18 0 R /BitsPerComponent 8 /Filter /FlateDecode of Computer Science, Lund University 2 axiomatic vs naïve set theory Zermelo-Fraenkel Set Theory w/Choice (ZFC) extensionality regularity specification union replacement infinity power set choice This course will be about “naïve” set theory. /Parent 10 0 R We remind readers that there are vital topics from those two areas that some schools will include in courses with titles like "discrete structures" and "discrete mathematics"; some will require one course, others two. Two sets are equal if and only if they have the same elements. Functions Definitions and Examples Subsection 1 Definitions and Examples George Voutsadakis (LSSU) Discrete Structures for Computer Science August 2018 3 / 66. Sets in Discrete Structures By . 13 0 obj << x�U�?O�0��~���DL|�����P��A��J�b�I����s�#�S|�{�w�~�W��\g�0�Jfu�q!���d�Ye����;�
G��\��؞�R��S3��R�b�6$������`�I��D?�-�V(i��M9�[ Differentiate between dependent and independent events. Discrete Mathematics is a branch of mathematics involving discrete elements that uses algebra and arithmetic. endobj