FREE IGNOU BCA NOTES MCS-013

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1 FREE IGNOU BCA NOTES MCS-013 UNIT 1 PROPOSITIONAL CALCULUS 1.2 PROPOSITIONS Table 1: Truth table for disjunction Table 3: Truth table for implication Table 4: Truth table for two-way implication.Table OBJECTIVES Table 9: Truth table for ‘exclusive or’Unit-1 UNIT 1 SETS, RELATIONS AND FUNCTIONS Structure Page No.1.2 INTRODUCING SETS Fig. 3: Venn diagram for union Fig. 4: Venn diagram for intersection of sets(c) (d)Fig. 6: Venn diagram for Aʹ.1.4 RELATIONS Now, you know that the multiplication of numbers is commutative. Is the Cartesian product of sets also commutative? For instance, is {1}×{2}={2}×{1}? No, because 1.4.2 Relations and FUNCTIONS The rule f is a function Fig.9: The rule f is not a function Fig.10: The rule is not a function Types of Functions There is a particular kind of bijective function that we use very often. Let us define this. Definition: A bijective mapping f : A( A is said to be a permutation on the set A. Let A = {a1,a2,…,an}, and f be a bijection from A onto A that maps ai to f(ai), then we write f as Now we can see how different operations like addition, subtraction, multiplication and division can be applied on functions Operations on Functions Unit-2 UNIT 2 METHODS OF PROOF OBJECTIVES After reading this unit, you should be able to develop in your learners the ability to:Convincing evidence is also what the world asks for before accepting a scientist’s predictions, or a historian’s claims.Why don’t you check an argument for validity now?Check whether the following argument is valid For example, Unit-2 UNIT 2 COMBINATORICS INTRODUCTION OBJECTIVES MULTIPLICATION AND ADDITION PRINCIPLES PERMUTATIONS COMBINATIONS BINOMIAL COEFFICIENTS COMBINATORIAL PROBABILITY Unit-3 UNIT 3 BOOLEAN ALGEBRA AND CIRCUITS3.1OBJECTIVESFig. 18Fig. 6: Diagrammatic representation of an AND -gate Fig. 7: Diagrammatic representation of an OR-gateFig. 8: Diagrammatic representation of NOT-gate Fig. 10Fig. 16Fig. 19Unit-33.0 INTRODUCTION3.1 OBJECTIVES3.2 PIGEONHOLE PRINCIPLE 3.3 INCLUSION-EXCLUSION PRINCIPLE3.4 APPLICATIONS OF INCLUSION-EXCLUSION 4UNIT 4PARTITIONS AND DISTRIBUTIONS4.0INTRODUCTION4.1OBJECTIVESINTEGER

FREE IGNOU BCA NOTES MCS-013 UNIT 1 PROPOSITIONAL CALCULUS 1.2 PROPOSITIONS Table 1: Truth table for disjunction Table 3: Truth table for implication Table 4: Truth table for two-way implication.Table  OBJECTIVES Table 9: Truth table for ‘exclusive or’Unit-1 UNIT 1 SETS, RELATIONS AND FUNCTIONS Structure Page No.1.2 INTRODUCING SETS Fig. 3: Venn diagram for union Fig. 4: Venn diagram for intersection of sets(c) (d)Fig. 6: Venn diagram for Aʹ.1.4 RELATIONS Now, you know that the multiplication of numbers is commutative. Is the Cartesian product of sets also commutative? For instance, is {1}×{2}={2}×{1}? No, because 1.4.2 Relations and FUNCTIONS  The rule f is a function Fig.9: The rule f is not a function Fig.10: The rule is not a function Types of Functions There is a particular kind of bijective function that we use very often. Let us define this. Definition: A bijective mapping f : A( A is said to be a permutation on the set A. Let A = {a1,a2,…,an}, and f be a bijection from A onto A that maps ai to f(ai), then we write f as Now we can see how different operations like addition, subtraction, multiplication and division can be applied on functions Operations on Functions Unit-2 UNIT 2 METHODS OF PROOF OBJECTIVES After reading this unit, you should be able to develop in your learners the ability to:Convincing evidence is also what the world asks for before accepting a scientist’s predictions, or a historian’s claims.Why don’t you check an argument for validity now?Check whether the following argument is valid For example, Unit-2 UNIT 2 COMBINATORICS INTRODUCTION OBJECTIVES MULTIPLICATION AND ADDITION PRINCIPLES PERMUTATIONS COMBINATIONS BINOMIAL COEFFICIENTS COMBINATORIAL PROBABILITY Unit-3 UNIT 3 BOOLEAN ALGEBRA AND CIRCUITS3.1OBJECTIVESFig. 18Fig. 6: Diagrammatic representation of an AND -gate Fig. 7: Diagrammatic representation of an OR-gateFig. 8: Diagrammatic representation of NOT-gate Fig. 10Fig. 16Fig. 19Unit-33.0 INTRODUCTION3.1 OBJECTIVES3.2 PIGEONHOLE PRINCIPLE 3.3 INCLUSION-EXCLUSION PRINCIPLE3.4 APPLICATIONS OF INCLUSION-EXCLUSION 4UNIT 4PARTITIONS AND DISTRIBUTIONS4.0INTRODUCTION4.1OBJECTIVESINTEGER

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