DeMorgan's Law
DeMorgan's Law of Conjunction.
What is ~(P ∧ Q) ≡ ~P ∨ ~Q ?
The equivalence below is either true or false.
(P→Q) ≡ (~Q→~P)
What is True?
The truth table for (P→Q) ∨ Q.
What is
T
F
T
T
The symbol for intersection (finding the common elements in two sets)
What is ⋂?
Type of words that are in universally quantified statements.
What is every, all, for every, for all, etc.?
DeMorgan's Law of Disjunction.
What is ~(P ∨ Q) ≡ ~P ∧ ~Q ?
The equivalence below is either true or false.
(P→Q) ≡ (Q→P)
What is False?
The truth table for [(P ∨ Q) ∧ (P ∨ ~Q)] ∨ P.
What is
T
T
F
F
Let A = {2,4,6,8,10} and B = {4,8,10}.
The difference between A and B (Find A - B)
What is A - B = {2,6}?
Describe how to negate an existentially quantified statement.
What is...
"Change it to a universally quantified statement and negate the statement."
The standard form negation of the following statement:
"I created Pokermon and my name is not Brock."
What is...
"I did not create Pokermon or my name is Brock."
Let (P→Q) be the following conditional statement:
If Jason is the Phoenix King, then the logic class must bow down before him.
The below argument is valid or invalid:
The logic class must bow down before Jason. Therefore, Jason is the Phoenix King.
What is Invalid?
(P ∧ Q) ∧ (~P ∨ ~Q) is either a tautology, contradiction, or neither. (Show worked out truth table).
What is a contradiction?
Let A = {5,10,15}, B = {4,8,12,16}, and C = {10,12,14,16,18}
Find (𝐴 ⋃ 𝐵) ⋂ C.
What is {10,12,16}?
Negate the following:
"There exists a bad student in this class room."
What is...
"Every student in this class is not a bad student."
The standard form negation of the following statement:
"Jason ruined my cabbages or Jason doesn't like to play air ball."
What is...
"Jason did not ruin my cabbages and Jason does like to play air ball."
The contrapositive of the following conditional statement:
"If I like chickie nuggies, then I will like Chick-fi-La."
"If I will not like Chick-fi-La, then I do not like chickie nuggies."
[(P → Q) ∧ ~P] → ~Q is either a valid argument or an invalid argument. (Show truth table)
What is an invalid argument?
A= {2,6,7}, B = {1,3,4 6,7}, and C = {5,6,7,8,15}.
Find (𝐵 − 𝐴) ⋂ (A ⋃ 𝐶).
{}
Negate the following:
"All of the bananas in the universe are not purple."
What is...
"There exists a banana in the universe that is purple."