2.6. Truth Tables http://www.ck12.org
We would write “pandq” asp∧qand “porq” asp∨q.
Truth tables use these symbols and are another way to analyze logic. First, let’s relatepand∼p. To make it easier,
setpas:An even number.Therefore,∼pisAn odd number. Make a truth table to find out if they are both true.
Begin with all the “truths” ofp, true (T) or false (F).
TABLE2.5:
p
T
FNext we write the corresponding truth values for∼p.∼phas the opposite truth values ofp. So, ifpis true, then
∼pis false and vise versa.
TABLE2.6:
p ∼p
T F
F TTo Recap:
- Start truth tables with all the possible combinations of truths. For 2 variables there are 4 combinations for 3
variables there are 8.Youalwaysstartatruthtablethisway. - Do any negations on the any of the variables.
- Do any combinations in parenthesis.
- Finish with completing what the problem was asking for.
Example A
Draw a truth table forp,qandp∧q.
First, make columns forpandq. Fill the columns with all the possible true and false combinations for the two.
TABLE2.7:
p q
T T
T F
F T
F FNotice all the combinations ofpandq.Anytime we have truth tables with two variables, this isalways how we
fill out the first two columns.
Next, we need to figure out whenp∧qis true, based upon the first two columns.p∧qcan only be true if BOTHp
andqare true.So, the completed table looks like this: