Notes - Truth Tables fun, fun, and more fun!!!!

A compound statement is created by combining two or more statements, p and q.

Conjunction uses the word “ and” Symbol ^ True only when all parts are true

Disjunction uses the word “or” Symbol v True if any one of its parts are true

truth table a table that lists all possible combinations of truth values ****Be sure to include all possible combinations of truth values for each piece of the compound statement***

Conjunction pqp ^ q TTT TFF FTF FFF

Disjunction pqp v q TTT TFT FTT FFF

Negation p~p TF FT

A statement whose truth table contains only True in the final column is a tautology A statement whose truth table contains only False in the final column is a contradiction

Conditional – think only time false is a broken promise pqp q TTT TFF FTT FFT

Example 1. ~(p v q) pq TT TF FT FF

pqp v q~(p v q) TTTF TFTF FTTF FFFT

Example 2. p ^ ~q pq TT TF FT FF

pq~ qp ^ ~q TTFF TFTT FTFF FFTF

Ex 3. (p ^ q) q pq TT TF FT FF

pqp ^ q (p ^ q) q TTTT TFFT FTFT FFFT

Ex 4. (p v q) ~p pq TT TF FT FF

pqp v q~ p (pvq) ~p TTTFF TFTFF FTTTT FFFTT

(p ^ q) v (p ^ r) p T T T T F F F F

pqrp ^ qp ^ r (p ^ q) v (p ^ r) TTTTTT TTFTFT TFTFTT TFFFFF FTTFFF FTFFFF FFTFFF FFFFFf