Discrete Mathematics with Graph Theory (3rd Edition) 38

Discrete Mathematics with Graph Theory (3rd Edition) 38 -...

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Unformatted text preview: 36 Solutions to Exercises 31. George Boole (1815-1864) was one of the greatest mathematicians of the nineteenth century. He was the first Professor of Mathematics at University College Cork (then called Queen's College) and is best known today as the inventor of a subject called mathematical logic. Indeed he introduced much of the symbolic language and notation we use today. Like Charles Babbage and Alan Turing, Boole also had a great impact in computer science, long before the computer was even a dream. He invented an algebra of logic known as Boolean Algebra, which is used widely today and forms the basis of much of the internal logic of computers. His books, ''The Mathematical Analysis of Logic" and "An Investigation of the Laws of Thought" form the basis of present-day computer science. Exercises 2.3 1. [BB] S x B is the set of ordered pairs (8, b), where 8 is a student and b is a book; thus, S x B represents all possible pairs of students and books. One sensible example of a binary relation is { ( represents all possible pairs of students and books....
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