Presentation on theme: "Constructing a Truth Table"— Presentation transcript:
1 Constructing a Truth Table Logic: Truth TablesConstructing a Truth Table
2 Truth 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.
3 RowsTo 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.
4 ColumnsThe columns under the connectives /\, and \/, stand for the conjunction, and disjunction of the expression on the two sides of that connective.
5 Two 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
6 The 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.
7 Negation Truth Table p ~ p The opposite of p is ~p T F “Not true” is “false”“Not false” is “true”
8 Conjunction Truth Table pqp /\ qp and qTTrue only if both are true.F
9 Disjunction Truth Table pqp \/ qp or qTTrue if either on is trueFFalse only if both are false
10 Lets fill out a tablepq\/(or)(~p(not)/\(and)q)TF
15 Fill in the \/ column using the p and the /\ columns qP\/(or)P and (~p/\p)(~p(not)/\(and)(~p) and (p)TF
16 Use the final column to determine what type of statements it is \/(or)P and (~p/\p)TautologyAlways TrueContradictionAlways FalseContingencySometimes true, sometimes falseTxF
17 Contingency Some were true, while one was false. That makes this statement a contingency.
18 Real 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.
19 Only on if both are closed Series CircuitsSwitch pSwitch qLightClosedOnOnly on if both are closedOpenOff
20 Only off when both are open Parallel CircuitsSwitch pSwitch qLightClosedOnOpenOffOnly off when both are open
21 Conclusion That concludes the Logic: Truth Tables lesson. For more information, consult Finite Mathematics by Berresford and Rockett.Or learn logic online: