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• PDF Name: Discrete Mathematics
• Book’s Language: English
• Pages: 139
• File Size: 1.54 MB
• PDF File Name: Discrete-Mathematics.pdf
• Category of the Book: Education

## Summary of Discrete Mathematics

“Discrete Mathematics” Highlights

1. Discrete mathematics is the subject of the document.
2. Discrete mathematics studies countable and finite sets, logical assertions, algorithms, graphs, and relations.
3. It introduces discrete mathematics’ core concepts and principles.
4. Sets, relations, functions, propositional and predicate logic, mathematical induction, combinatorics, and graph theory are covered.
5. Properties, operations, subsets, and set operations including union, intersection, and complement are addressed.
6. Reflexivity, symmetry, transitivity, equivalence relations, and partial orders are examined.
7. Domain, codomain, range, injectivity, surjectivity, bijectivity, composition, and inverse functions are investigated in functions.
8. Propositional logic introduces logical operators (AND, OR, NOT), truth tables, logical equivalences, and rules.
9. Predicate logic includes quantifiers (existential and universal), predicates, and logical connectives.
10. Mathematical induction proves all natural number properties.
11. Combinatorics covers permutations, combinations, binomial coefficients, and inclusion-exclusion.
12. Graph theory introduces graphs, vertices, edges, routes, cycles, trees, planarity, and graph coloring.
13. Examples, images, and exercises help explain the subject.
14. Computer science, cryptography, and algorithms use discrete mathematics.