Statements, Negations, Conjunctions & Disjunctions
"The sky is blue."
What is a statement?
Implication or conditional?
(p /\ q)->(q \/~p)
What is a conditional statement?
A property of two statements if and only if they have identical truth tables.
What is logical equivalence?
____ always lie and ____ always tell the truth.
What are knights and knaves?
Any declarative sentence that is either true or false, but not both.
What is a statement?
A statement that is true if and only if both P and Q are true.
What is a conjunction?
Implication or conditional?
[(p->q) /\ p]->q
What is an implication?
if P is logically equivalent to Q, and Q is logically equivalent to R, then P is logically equivalent to R.
What is the transitive property?
A conditional statement that is a tautology.
What is an implication?
A statement that is always false.
What is a contradiction?
A statement whose truth value is the opposite of the truth value of P.
What is a negation?
A conditional statement where the antecedent and consequent are exchanged.
What is the converse?
"If P, then Q", is logically equivalent to "If not Q, then not P."
What is the contrapositive?
Tautology or Contradiction?
[(p->q)/\ ~p]-?~q
What is neither a tautology or contradiction?
A statement that is always true.
What is a tautology?
A statement that is true if and only if at least one of P and Q is true.
What is a disjunction?
The first part of a conditional statement (in most cases P).
What is the antecedent?
~(P /\ Q) is logically equivalent to ~P \/ ~Q.
What is DeMorgan's Law of Conjunction?
Tautology or contradiction?
[(p->q) /\ ~q] /\ p
What is a contradiction?
A statement read as "If P, then Q".
What is a conditional statement?
A diagram used to show the truth values of different statements and compound statements.
What is a truth table?
When a true statement leads to a false statement in a conditional statement.
When is a conditional statement false?
Given and statement, part of the statement can be substituted by a logically equivalent statement without affecting the true value of the original statement.
Tautology or contradiction?
[(p -> q) /\ ~q]-> ~p
What is a tautology?
A statement that is true if and only if the two statements have identical truth values.
What is a biconditional statement?