Review for Midterm
Fall 2021
Title
Ch/Sec
1
Rev
Page
Formal Logic
1.1
Statements, Symbolic Rep
and Tautologies
16
1.2
Propositional Logic
35
1.4
Quantifiers, Predicates and
Validity
Predicate Logic
1.6
Proof of Correctness
1.3
2
50
69
92
Proof Techniques
107
2.2
Induction
More on Proof of
Correctness
122
Number Theory
153
2.4
3
137
Recursive Definitions
171
3.2
Recurrence Relation
197
3.3
Analysis of Algorithms
213
Sets
239
4.2
Counting
Inclusion/Exclusion,
Pigeonhole Principles
Permutations and
Combinations
258
4.4
Table 1.7, p.59
Counterexamples; direct proof, proof by contraposition, proof by
contradiction
First, Second principle of Induction.
Verify correctness of a program segment that includes a loop
statement.
gcd function, write gcd(a,b) as a linear combination of a and b; prime
factorization; Euler phi function.
Table 2.2, p.106
Table 2.3, p.114
Use a recursive definition of a sequence; Find recursive definitions;
write recursive algorithm.
Closed-form solutions; solve recurrence relations by expand, guess and
verify; solve linear 1-st order with constant coefficients and solve
divide-and-conquer recurrence relations using a respective formula.
Worst-case analysis from a recurrence relation.
Table 3.2, p.184
Table 3.5, p.196
Sets and Combinatorics
4.1
4.3
Truth value of a predicate wff in an interpretation; recognize
valid/invalid wwf.
Derivation rules; prove validity of an argument.
Verify correctness of program segments that uses assignment
statement; conditional statement.
Table 1.5, p.4
Table 1.6, p.5
Table 1.11, p.28; Table 1.12, p.29;
Table 1.14, p.37
Recursion, Recurrence Relations, and Analysis of Algorithms
3.1
4
Construct truth tables for compound wff’s; recognize tautologies and
contradictions.
Derivation rules, validity of a verbal argument.
Proofs, Induction and Number Theory
2.1
2.3
Topics
269
288
Definitions, set operations, subset, power set, Cartesian product,
identities, countable and uncountable sets.
Multiplication principle, addition principle, decision trees.
Use to find number of elements in a union set; find the minimum
number of elements to guarantee two in a duplicative property.
Use P(n,r) and C(n,r) along with Mult and Add Principles; not all
distinct; repetition allowed.
Table 4.2, p.280