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# review1 - (l Expressing implication and biconditionals(pg...

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REVIEW SHEET FOR EXAM 1 (1) Sets (a) Empty set (b) Subsets (c) Notation for sets (page 15) (d) Indexed collections of sets. (e) Partitions of sets. (f) Set operations. (g) Power sets. (h) Sets as elements of other sets. (i) Difference between elements and subsets. (j) Cartesian products. (2) Logic (a) What is a statement? (b) What is an open sentence? (c) Definition of tautology and contradiction. (d) Examples of tautology and contradiction. (e) Negating statements. (f) Using quantifiers. (g) Negating statements with quantifiers. (h) Disjunction, conjunction, implication. (i) Biconditional. (j) Logical equivalence. (k) Characterizations of statements.
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Unformatted text preview: (l) Expressing implication and biconditionals (pg. 40, 43) (m) Converse, Contrapositive (3) Direct Proof and Contrapositive (a) Be able to prove statements about even, odd integers, divisibility, con-gruences, real numbers, sets. (4) Proof by contradiction (a) Be able to prove statements about even, odd integers, divisibility, con-gruences, real numbers, sets, rational and irrational numbers, etc. (b) Problems: 5.1–5.24 (5) Proof evaluations (a) Problems: 3.27, 3.28, 3.29, 3.30, 3.41, 4.58, 4.59, 4.60, 4.61, 4.62, 4.63, 4.645.43, 5.44, 5.45, 5.46 1...
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