The Basics
A declarative sentence that is either true or false, but not both.
statement
The negation of the statement "The sky is blue."
"The sky is not blue"
The number of rows required in a truth table for a statement with 3 distinct variables (p, q, and r).
8
This variation of the conditional statement p → q is formed by negating and swapping both components: ~q → ~p.
Contrapositive
According to De Morgan's Law, the statement ~(p ∧ q) is equivalent to this.
~p V ~q
What is the logical connective represented by the symbol V
OR
The negation of the statement "All prime numbers are odd."
"Some prime numbers are not odd"
"At least one prime number is not odd"
*Could use "even" instead of "not odd"
The only truth value combination for p and q that makes the implication p → q false.
TF
The name for the variation of
p → q written as q → p.
Converse
According to De Morgan's Law, the statement ~(p V q) is equivalent to this.
~p ∧ ~q
The truth value of the conjunction p ∧ q when p is True and q is False
False
What is the negation of "It is snowing or it is windy."
"It is not snowing and it is not windy"
The "fancy" name for when a compound statement that is always true, regardless of the truth values of the individual statements.
Tautology
The name for the variation of p → q,
written as ~p → ~q.
Inverse
The simplified equivalent statement ~(~p ∧ q).
p V ~q
The symbolic representation of the phrase "p if and only if q."
⟺
What is the negation of "Some students are passing."
"No students are passing" or "All students are not passing"
Complete the Truth Table:
p | q | p ∧ q
T T
T F
F T
F F
T
F
F
F
Write the contrapositive of:
"If I am talking, then I am busy."
"If I am not busy, then I am not talking."
Simplify the following: ~(~t → ~s)
~t ∧ s
Let q, h, and c represent the following simple statements:
q: I complete all the work.
h: I get a C or higher.
c: I get college credit.
Write the following as a complete sentence: (q → h) ∧ c
If I complete all the work then I get a C or higher, and I get college credit.
Write the symbolic negation of the
conditional p → q
p ∧ ~q
A statement that is always false, such as p ∧ ~p
(opposite of a Tautology)
Contradiction
Write the contrapositive of the following: p → (~r V s)
(r ∧ ~s) → ~p
The Bears score more points AND the Bears do not win.