Use a truth table to determine whether the argument is valid or invalid.
Whether the given argument is valid or invalid using the truth table
An Argument and a Valid Argument: An argument consists of a set of statements called premises and another statement called the conclusion. An argument is valid if the conclusion is true whenever all the premises are assumed to be true. An argument is invalid if it is not a valid argument.
The following truth table procedure can be used to determine whether an argument is valid or invalid.
Truth Table Procedure to Determine the Validity of an Argument:
|The negation of statement p is "not p." The negation of p is symbolized by "~p." The truth value of ~p is the opposite of the truth value of p.|
|A disjunction is a compound statement formed by joining two statements with the connector OR. The disjunction "p or q" is symbolized by . A disjunction is false if and only if both statements are false; otherwise it is true.|
|A conjunction is a compound statement formed by joining two statements with the connector AND. The conjunction "p and q" is symbolized by . A conjunction is true when both of its combined parts are true; otherwise it is false.|
|A conditional statement, symbolized by , is an if-then statement in which p is a hypothesis and q is a conclusion. The logical connector in a conditional statement is denoted by the symbol . The conditional is defined to be true unless a true hypothesis leads to a false conclusion.|
|A biconditional statement is defined to be true whenever both parts have the same truth value. The biconditional operator is denoted by a double-headed arrow . The biconditional represents "p if an only if q", where p is a hypothesis and q is a conclusion.|