Blog 4

Todays lecture will be on truth tables. A truth table is a listing of all possible combinations of the individual statements of an argument as either true or false as well are the resulting truth values of the compound statement. In other words, by using a truth table we can determine the truth-values of an argument. The statement will be presented as either a ‘and’ , ‘or’ or an Ifàthen statement. For example: If you give me five dollars, then I will pay you back. There are several forms of truth tables for the different types of statements. These truth value forms include:

P	~P
T	F
F	T

~P                                             

  P and Q                                    (P^Q)

P	Q
T	F
T	T
F	T
F	F

P	Q	P^Q
T	F	F
T	T	T
F	T	F
F	F	F

                                   

P	Q	PvQ
T	T	T
T	F	T
F	T	T
F	F	F

P	Q	PàQ
T	T	T
T	F	F
F	T	T
F	F	T

  (PvQ) Disjunction                                 (PàQ) Conditional

            The last table is the conditional table. It is used for Ifàthen statements such as the example statement: If you give me five dollars, then I will pay you back. In this statement:

P=you give me five dollars

Q=I will pay you back

            The truth table for this statement would be set up at first like:

P	Q
T	T
T	F
F	T
F	F

The next step would to do the truth table of PàQ which would look like:

P	Q	PàQ
T	T	T
T	F	F
F	T	T
F	F	T

Thus the statements truth values are T, F, T, T. Thus the only instance in which the statement is false is when: If you give me five dollars, then I do not pay you back.