First Day Definitions
Logic Symbols
Set Builder Notation
Set Logic
100
What is the definition of a positive integer?
An integer x > 0.
100
What is the truth table for
P ↔ Q ?
T
F
F
T
100
Write using set builder notation, the set of positive integers
{xεZ : x>0 }
100
What does x ε (A U B) mean?
x ε A or xεB
200
What is the definition of an Even Number?
An integer x, s.t. 2|x is true.
200
Is P → Q ⇔ (¬Q) → (¬P) true?
Yes! This statement even has a fancy name, Proof by Contrapositive!
200
Write using set builder the set of odd negative integers
{ xεZ : x<0 ^ x is odd}
200
What is the difference of two sets?
A-B
For xεA-B,
x is in A and not in B.
300
What does it mean if a divides b? Provide definition and the mathematical symbol that defines the statement.
a|b
a divides b means there exists a third integer c, s.t. b = a*c
300
When is an If-Then statement false?
P → Q
An If-Then statement is only false when the initial condition is true and the second condition is false.
300
Write the set of prime numbers using set builder
{x: x is prime}
300
A ∪ (B ∩ C)= ?
(A ∪ B) ∩ (A ∪ C)
400
What does it mean if p is prime?
If p is prime, p>1 and 1 and p are its only divisors.
400
List a distributive property of logic symbols
P ∧ (Q ∨ R) ⇔ (P ∧ Q) ∨ (P ∧ R)
or
P ∨ (Q ∧ R) ⇔ (P ∨ Q) ∧ (P ∨ R)
400
What is the symbol for the empty set?
Either {} or 
400
What is the symmetric difference of two sets?
AΔB
For xεAΔB,
x is in only A or x is in only B.
500
What is a Lemma?
A lemma is a theorem that is used primarily to help solve another theorem.
500
List one of DeMorgan's Laws using logic symbols?
¬(P ∨ Q) ⇔ (¬P) ∧ (¬Q)
or
¬(P ∧ Q) ⇔ (¬P) ∨ (¬Q)
500
The set of complex numbers with an imaginary part
{zεC: z NOT ∈ R}
500
How do you show set A is equal to set B?
First show A ⊆ B. Then show B ⊆ A.