Sydney Silverman

Blog 4

Truth Tables

·      Truth tables are mathematical tables used in logic

·      Truth tables can be used to determine if a complicated statement is true or false based on the truth or falsity of its simple components

·      Truth tables- listing of all possible truth values of a compound statement with all the possible combinations of the individual statements

·      Truth values- classification of a statement

(~) represents a negation               

            Truth table for p

(^) represents a conjunction

            Truth table for (p^q)

p	q	p^q
T	T	T
T	F	F
F	T	F
F	F	F

P	~P
T	F
F	T

(v) represents a disjunction

            Truth table for (pvq)

p	q	pvq
T	T	T
T	F	T
F	T	F
F	F	T

(  ) represents conditionals

            Truth table for (p  q)

p	q	p  q
T	T	T
T	F	F
F	T	T
F	F	T

Truth Values for p and q

p	q
T	T
T	F
F	T
F	F

Rules:

·      1 argument- 2 rows

·      2 arguments- 4 rows

·      3 arguments- 8 rows

Example:

p: you give me a ride to work

q: I give you gas money

(p q) If you give me a ride to work, then I give you gas money

There are two options-

a)    I gave you gas money (I kept my promise)

b)    I do not give you gas money (I did not keep my promise)

·      Suppose p is true:

p	q	p  q
T	T	T
T	F	F

·      Suppose p is false:

p	q	p  q
F	T	T
F	F	T

By default p     q is always true, because it doesn’t matter if the conclusion “q” is true or false if the premise is false

Example 2:

p: Charles did wash his car

q: Charles did go to the library

(p^~q) Charles did wash his car, did not go to the library

Truth table for (p^~q)

p	q	~q	p^~q
T	T	F	F
T	F	T	T
F	T	F	F
F	F	T	F