Presentation on theme: "Constructing a Truth Table"— Presentation transcript:
1Constructing a Truth Table Logic: Truth TablesConstructing a Truth Table
2Truth TableA truth table for a compound statement is a list of the truth or falsity of the statement for every possible combination of truth and falsity of its components.In other words, a truth table helps to show whether a statement is true or false.
3RowsTo find the number of rows used in a truth table, take the number 2 raised to the power of the number of variables.For example, if there was a p statement and a q statement, there would be 2 variables, 2^2 is 4.If there were three statements, it would be 2^3, or 8 rows.
4ColumnsThe columns under the connectives /\, and \/, stand for the conjunction, and disjunction of the expression on the two sides of that connective.
5Two statement table p q T Half the rows should be true The rows should alternate T, FFThe result should beHalf the rows should be falseone of every possibilityTT, TF, FT, FF
6The three statement table pqrTHalf of the rowsAlternate TTAlternateshould be true,and FFFT and Fthe other halfso that there isshould be false.one of everypossibilityTTT, TTF, TFTect.
7Negation Truth Table p ~ p The opposite of p is ~p T F “Not true” is “false”“Not false” is “true”
8Conjunction Truth Table pqp /\ qp and qTTrue only if both are true.F
9Disjunction Truth Table pqp \/ qp or qTTrue if either on is trueFFalse only if both are false
10Lets fill out a tablepq\/(or)(~p(not)/\(and)q)TF
15Fill in the \/ column using the p and the /\ columns qP\/(or)P and (~p/\p)(~p(not)/\(and)(~p) and (p)TF
16Use the final column to determine what type of statements it is \/(or)P and (~p/\p)TautologyAlways TrueContradictionAlways FalseContingencySometimes true, sometimes falseTxF
17Contingency Some were true, while one was false. That makes this statement a contingency.
18Real life exampleIn case that was not entirely clear, let’s take a look at an everyday example.Circuits. There are two different kinds of circuits, a series circuit and a parallel circuit.When the switch is closed the light will be on. However, with a series circuit, both switches have to be closed and with a parallel circuit only one switch has to be closed for the light to go on.
19Only on if both are closed Series CircuitsSwitch pSwitch qLightClosedOnOnly on if both are closedOpenOff
20Only off when both are open Parallel CircuitsSwitch pSwitch qLightClosedOnOpenOffOnly off when both are open
21Conclusion That concludes the Logic: Truth Tables lesson. For more information, consult Finite Mathematics by Berresford and Rockett.Or learn logic online: