V. REAL NUMBER SYSTEM
A . Subsets of the real numbers
1. Natural numbers
a) Primes
b) Composites—prime factorization
2. Integers
a) Multiples and divisors
i. Factors
ii. Divisibility
iii. Least common multiple
iv. Greatest common divisor
v. Perfect squares
b) Odd and even integers
3. Rational and irrational numbers
a) Decimal representations
b) Simplification of radicals and exponents
c) Identifying rational and irrational numbers
B . Operations and properties
1. Properties of the binary operations
a) Closure
b) Commutative properties
c) Associative properties
d) Distributive properties
2. Absolute value
3. Real number line
a) Order
b) Density
c) Completeness
4. Properties of zero and one
a) Identity elements
b) Additive and multiplicative inverses
c) Division involving zero
d) Zero as an exponent
5. Nature of the roots of quadratic equations
6. Pythagorean triples

VI. LOGIC
A . Propositions
1. Simple statements
a) Symbols
b) Quantifiers (all, some)
2. Negation
3. Compound statements
a) Conjunction
b) Disjunction
c) Implication (conditional statements)
i. Necessary conditions
ii. Sufficient conditions
iii. Equivalence (necessary and sufficient conditions)
d) Derived implications
i. Converse
ii. Inverse
iii. Contrapositive
B . Truth tables
C . Methods of proof
1. Valid arguments
a) Direct
b) Indirect—contradiction and counterexample
2. Invalid arguments—fallacies