STOR 215

Study Guide for Midterm 1

1.
Propositions: simple and compound; truth values, truth tables

2. Basic logical operations: and, or, not, conditional and biconditional statements

3. Converse, contrapositive, and inverse of conditional statements

4. Translation: from logical expressions to English sentences, and vice versa

5. Propositional equivalence: contradiction, tautology, basic logical equivalences

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 and maxima

10. Sets: description, subset, element of, emptyset

11. Basic set operations: union, intersection and complement; disjoint sets.

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.