Standard Forms
The standard form of ~(~P).
What is P?
A statement that is always true.
What is a tautology?
⇒ read out loud in English.
What is "implies?"
The definition of a statement.
What is: "A declarative sentence that is either true or false, but not both?"
DeMorgan's Law of Conjunction.
What is ~(P ∧ Q) ≡ ~P ∨ ~Q?
The reason why P ∧ ~P is a contradiction.
What is: "Because P and ~P can't be true at the same time."
When P → Q is a tautology, where P and Q are statements.
What is an implication?
When two statements have the same (identical) truth table.
What is logically equivalent?
The standard form of ~(P ∨ Q).
What is ~P ∧ ~Q?
P ∨ (Q ∨ ~P) is either a tautology or a contradiction (No work is necessary).
What is a tautology?
Any implication you can think of stated out loud.
Did Jason like the answer?
The inverse of the following conditional statement: "If trees do not have leaves, then it is winter."
What is... "If trees do have leaves, then it is not winter?"
The negation of the following statement: "The Yankees are a baseball team and the Jazz is a basketball team."
What is... "The Yankees are not a baseball team or the Jazz is not a basketball team."
Show (P → Q) ∨ (Q → P) is a tautology, contradiction, or neither by making a truth table.
What is a tautology?
The only time when P → Q is false.
What is, "When P is true and Q is false?"
The converse of the following conditional statement: "If I am the master of logic, then I am the master of math."
What is... "If I am the master of math, then I am the master of logic."
The negation of the following conditional statement: "If seven is odd, then seven is not even."
What is... "Seven is odd and seven is even?"
Show that (P → Q) ∧ [~(~Q → ~P)] is a tautology, contradiction, or neither by using a truth table.
What is a contradiction?
Show if [(P → Q) ∧ P] → Q is an implication or not by using a truth table.
What is an implication?
The truth table for the biconditional statement (P ↔ Q).
What is the correct truth table?