Lectures1-3_2004 - Ling 726: Mathematical Linguistics,...

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Unformatted text preview: Ling 726: Mathematical Linguistics, Lectures 1-3 V. Borschev and B. Partee, September 9, 2004 p. 1 Lectures 1-3. Basic Concepts of Set Theory, Functions and Relations 0. Goals........................................................................................................................................................... 1 1. Basic Concepts of Set Theory. ................................................................................................................... 1 1.1. Sets and elements ................................................................................................................................ 1 1.2. Specification of sets............................................................................................................................. 2 1.3. Identity and cardinality........................................................................................................................ 3 1.4. Subsets................................................................................................................................................. 4 1.5. Power sets........................................................................................................................................... 4 1.6 and 1.7. Operations on sets: union, intersection, difference, complement............................................ 4 1.8. Set-theoretic equalities ........................................................................................................................ 8 Homework 1................................................................................................................................................... 8 2. Relations and Functions ............................................................................................................................. 9 2.1. Ordered pairs and Cartesian products.................................................................................................. 9 2.2. Relations.............................................................................................................................................. 9 2.3. Functions ............................................................................................................................................11 2.4. Compositions......................................................................................................................................12 Homework 2..................................................................................................................................................13 3. Properties of Relations ..............................................................................................................................13 3.1. Reflexivity, symmetry, transitivity, and connectedness .....................................................................13 3.2. Diagrams of relations..........................................................................................................................14 3....
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Lectures1-3_2004 - Ling 726: Mathematical Linguistics,...

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