Study Guide for Midterm 1
1. Propositions: simple
and compound; truth values, truth tables
2. Basic logical operations: and, or, not, conditional and
3. Converse, contrapositive, and inverse of conditional statements
4. Translation: from logical expressions to English sentences, and
5. Propositional equivalence: contradiction, tautology, basic
6. Predicates and quantifiers (universal and existential): logical
equivalence and De Morgan's rules
7. Nested quantifiers: understanding, negation, and translation
8. Proofs: direct, contrapositive, contradiction, exhaustive,
existence, and equivalence
9. Even and odd integers, rational numbers, absolute value, minima
10. Sets: description, subset, element of, emptyset
11. Basic set operations: union, intersection and complement;
12. Set identities: De Morgan and distributive laws.
13. Functions: domain, range, image, pre-image, one-to-one, onto,
bijection, increasing, decreasing.
14. Composition, addition, and multiplication of functions.
15. Floor and ceiling functions.
16. Series and summations.