PHL 3000 Lecture 7: Module 7: Truth Tables for Determining Validity
Lecture 7.1: Truth Tables for Determining Validity
Creating Truth Tables for Arguments:
• The procedure here is just like what we have been doing, only there will be one table that
contains all the premises and the conclusion
• P c Q ; P ; … Q (… = therefore)
o Cannot have entirely true premises and a false conclusion
▪ Looking for a row with true premises and a false conclusion
o
o Valid
• An argument is valid if and only if it is not possible for the premises to be true and the
conclusion false. A truth table is a representation of all possibilities with regard to the
truth of the premises and conclusion
o If there is at least one row in which all of the premises are true and the conclusion
is false, then the argument is invalid
▪ Has an invalidating row
o If there is no such row, then the argument is valid.
▪ Doesn’t have to be a row with true premises and a true conclusion.
Truth Tables for Arguments: Examples
• ( A = B); (B c C); ~C; …~A
o
o Valid
• A * (B v C); C c ~ A; …A c C
o
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