UGC NET Computer Science & Applications: Discrete Structures & Optimization - Mathematical Logic (2)

@sweetyasaiyed5920 UGC NET Paper 2 Computer Science and Applications Code No.:(87) UGC NET CS Syllabus Link: https://comptechaholic.com/e-learning/ Pdf Link of Unit 1: Discrete Structures and Optimization - Topic 2: Sets and Relations https://comptechaholic.com/product/ugc-net-computer-science/ Unit 1: Discrete Structures and Optimization (PART: 2/7) Mathematical Logic: Topics Covered: Set Operations Representation and Properties of Relations Equivalence Relations Partially Ordering. Index: Set Cardinality of a Set Representation of a Set: Roster / Tabular Form and Set Builder Notation Types of Sets (12): Finite Set Infinite Set Empty Set / Null Set / Void Set Singleton Set / Unit Set Universal Set Power Set Equal Set Equivalent Set Overlapping Set Disjoint Set Set Operations (6): Set Union : U Set Intersection : ∩ Set Difference / Relative Complement of Set : A−B or 𝐴∖𝐵 Set Symmetric Difference : AΔB Set Complement Set Cartesian Product / Set Cross Product Set Partitioning Bell Numbers Relations Types of relations (5): Binary Relation Empty Relation / Void Relation Full Relation / Universal Relation Inverse Relation Identity Relation Reflexive Relation v/s Identity Relation Properties of Relations (6): Reflexive Relation Irreflexive Relation / Anti-Reflexive Relation Symmetric Relation Anti-Symmetric Relation Asymmetric Relation Transitive Relation Equivalence Relation Partially Ordering Number of possible relations on 2 sets: Representation of Relations(4): Relation as a Matrix Relation as a Directed Graph Relation as a Table Relation as a Mapping Function Inverse of a Function Composition of Functions Types of mapping(6): Injective mapping / One-to-one mapping Surjective mapping / Onto mapping Bijective mapping / One-to-one Correspondent mapping Non-Injective mapping / Many-to-one mapping Into mapping Non-Surjective mapping / One-to-Many mapping