http://www.ck12.org Chapter 2. Reasoning and Proof
This is how a truth table with two variables and their “and” column is always filled out.
Example B
Draw a truth table forp,qandp∨q.
First, make columns forpandq, just like Example A.
TABLE2.8:
p q
T T
T F
F T
F FNext, we need to figure out whenp∨qis true, based upon the first two columns.p∨qis true ifpORqare true,
or both are true.So, the completed table looks like this:
The difference betweenp∧qandp∨qis the second and third rows. For “and” bothpandqhave to be true, but for
“or” only one has to be true.
Example C
Determine the truths forp∧(∼q∨r).
First, there are three variables, so we are going to need all the combinations of their truths.For three variables,
there are always 8 possible combinations.
TABLE2.9:
p q r
T T T
T T F
T F T