Unit 2. Data presentation. Building truth tables
Unit 2. Data presentation. Building truth tables.
What is it?
What is it?
Solve a simple logical problem
Solve a simple logical problem.
4 cards are given. In the first and second cards, you see the front side with the numbers 5 and 8, the third and fourth cards have the reverse side, one has the blue side, and the other has the green one.
Task: if the card has an even number on the front side, then its reverse side is blue.
Question: What cards are needed to be turned over to check this statement?
http://lilac2012.livejournal.com/383811.html
The theme : How to build a truth table for a logical expression?
The theme: How to build a truth table for a logical expression?
Learning objectives:
10.2.2.2 build truth tables for a given logical expression
10.2.2.1 use logical operations (disjunction, conjunction, inversion)
Assessment criteria:
can build truth tables for a logical expression;
apply logical operations;
comply with the order of logical operations;
solve logical problems using truth tables.
Logical expressions to statements
Logical expressions to statements.
A printer, a monitor, and a plotter are information output devices.
А and В and С = F А & В & С = F A/\B/\C =F
Alan’s place at the Olympiad is not the first and not the last place.
F= ¬A/\¬B
I will choose physics or geography like the fourth subject on the UNT.
F=A\/B
TRUTH TABLE is a table that lists all possible values of the input logic variables and the corresponding values of the function
TRUTH TABLE is a table that lists all possible values of the input logic variables and the corresponding values of the function.
Where A, B are logical variables.
F is the result of a logical expression
А | B | F=А B |
0 | ||
1 | ||
1 | 0 | 1 |
А | B | F=А B |
0 | ||
1 | 0 | |
1 | 0 | |
А | F = А |
0 | 1 |
1 | 0 |
Algorithm for truth tables constructing
Algorithm for truth tables constructing
Determine the number of logical variables (for columns)
Determine the number of rows in the truth table (based on the number of logical variables and logical operations in the expression)
Write all possible values of logical variables (in lines)
Determine the number of logical operations and their order
Write logical operations in the truth table and determine for each value the corresponding logical variables.
Perform logical operations and calculate F
Example: A\/A/\B A B A/\B A\/A/\B 0 1 0 1 0 1 0 1
Example: A\/A/\B
A | B | A/\B | A\/A/\B |
0 | |||
1 | 0 | 1 | |
0 | 1 | 0 | |
1 | |||
Formula for determining the number of rows in the truth table where
Formula for determining the number of rows in the truth table
where N is the number of rows in the table
q - the number of logical variables in this expression
The procedure for actions in logical operations
The procedure for actions in logical operations
Inversion (logical negation)
Operations in brackets
Conjunction (logical multiplication)
Disjunction (logical addition)
Implication (following)
Equivalence (equality)
Build a truth table in pairs to the expression :
Build a truth table in pairs to the expression :
Build a truth table in pairs to the expression :
Build a truth table in pairs to the expression :
Check A B A\/B не A не B не
Check
A | B | A\/B | не A | не B | не A \/ не B | (A \/ B) & (не A \/ не B) |
0 | 1 | 0 | ||||
1 | 0 | 1 | ||||
1 | 0 | 1 | 0 | 1 | ||
1 | ||||||
Build a truth table for logical expressions independently
Build a truth table for logical expressions independently
F = B˅(B&A)
F = (A и не B) или (не A и B)
Reflection of achieving learning objectives
Reflection of achieving learning objectives
Resources http://sch8.edu.sbor
Resources
http://sch8.edu.sbor.net/logika.html
http://informatika.edusite.ru/lezione9_55.htm
Thank you for your attention!
Thank you for your attention!
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