PM_1 - Mathematics 131a - A Short But Fairly Complete Study...

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Unformatted text preview: Mathematics 131a - A Short But Fairly Complete Study Guide For Midterm 1 Exam Date: April 22, 2011 Instructor: D.E.Weisbart (1) Know the logical connectives and quantifiers, the truth tables for the quantifiers, and how to formally write the negations of statements. For example, you should be able to write down the negation of the statement defining the convergence of a sequence to a limit l . In addition, you should be able to prove the tautologies that give us our techniques of direct proof, proof by contrapositive, and proof by contradiction. (2) Know what a function is. Be able to state what it means for a subset of a cartesian product of two sets to define a well defined function. Be able to give an example of a well-defined function and a subset of the cartesian product of two sets that is not a well- defined function. Know the definition of 1-to-1 and onto. You should also know when the set theoretic inverse of a function is a well defined function....
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