Download presentation

Presentation is loading. Please wait.

1
**Constructing a Truth Table**

Logic: Truth Tables Constructing a Truth Table

2
Truth Table A 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
Rows To 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
Columns The 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, F F The result should be Half the rows should be false one of every possibility TT, TF, FT, FF

6
**The three statement table**

p q r T Half of the rows Alternate TT Alternate should be true, and FF F T and F the other half so that there is should be false. one of every possibility TTT, TTF, TFT ect.

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**

p q p /\ q p and q T True only if both are true. F

9
**Disjunction Truth Table**

p q p \/ q p or q T True if either on is true F False only if both are false

10
Lets fill out a table p q \/ (or) (~p (not) /\ (and) q) T F

11
Negate the p column p q \/ (or) (~p (not) /\ (and) q) T F

12
Copy the q column p q \/ (or) (~p (not) /\ (and) q) T F

13
Fill the /\ column p q \/ (or) (~p (not) /\ (and) q) T F

14
Copy the p column p q \/ (or) (~p (not) /\ (and) T F

15
**Fill in the \/ column using the p and the /\ columns**

q P \/ (or) P and (~p/\p) (~p (not) /\ (and) (~p) and (p) T F

16
**Use the final column to determine what type of statements it is**

\/ (or) P and (~p/\p) Tautology Always True Contradiction Always False Contingency Sometimes true, sometimes false T x F

17
**Contingency Some were true, while one was false.**

That makes this statement a contingency.

18
Real life example In 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 Circuits Switch p Switch q Light Closed On Only on if both are closed Open Off

20
**Only off when both are open**

Parallel Circuits Switch p Switch q Light Closed On Open Off Only 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:

Similar presentations

OK

2/17/2008Sultan Almuhammadi1 ICS 253-01 Logic & Sets (An Overview) Week 1.

2/17/2008Sultan Almuhammadi1 ICS 253-01 Logic & Sets (An Overview) Week 1.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on power system stability examples Free ppt on self development Ppt on electromagnetic field Ppt on college management system project Ppt on classification of resources and conservation Ppt on power diode data Ppt on atomic structure for class 8 Download ppt on cybercrime and security Download free ppt on active and passive voice Download ppt on eddy current brakes