Foundations of Mathematics (MATH 6100) Midterm Study Guide
Propositional Logic
1. Statements and variables (free and bound).
2. Logical operators: conjunction, disjunction, negation, implication, biconditional, and each of their truth tables.
3. Showing t
Foundations of Mathematics (MATH 6100) Midterm
Problems
1. (4 points) Populate the following truth table.
P
T
T
F
F
Q
T
F
T
F
P Q
P
Q
P
Q
2. (10 points) Unambiguously mark each of the following as true or false:
(a) P Q is equivalent to P Q.
(b) (P Q) is
Foundations of Mathematics (MATH 6100) Final Study Guide
Relations, Functions
1. Cartesian products. Denition of a relation. Denition of a function as a
special kind of relation. Parts of a function: name, domain, codomain, rule
of assignment. Familiarity
Foundations of Mathematics (MATH 6100) Final Exam
Name:
Problems
1. (2,2,1 points) Determine if the statements P Q and P Q are equivalent by constructing truth tables for each.
2. (5 points) Prove that if A B = A, then A B.
3. (10 points) If A, B, C are s