Constructing truth tables
Constructing truth tables
Learning objectives 10.2.2.2 construct truth tables for the given logical expression
Learning objectives
10.2.2.2
construct truth tables for the given logical expression
Lesson objectives
Consider the algorithm for constructing truth tables
Teach to construct a truth table
What types of statements are divided according to their structure? 2
1. What types of statements are divided according to their structure?
2. The truth of which statements is contractual?
3 What is the truth of the statements calculated?
4. How are simple sentences denoted in the algebra of sentences?
5. How is the truth of such statements indicated?
6. What connects variables in formulas of algebra of statements?
7. What are the logical operations?
Answering the questions that were on the first slide, try to formulate your own definition for truth tables
Answering the questions that were on the first slide, try to formulate your own definition for truth tables
A truth table is a breakdown of a logical function by listing all possible values that the function can attain
Specify the order of logical operations
Specify the order of logical operations.
1) Actions in brackets;
2) Negation (inversion);
3) Multiplication (conjunction);
3) Addition (disjunction);
А | В | ¬ A | ¬ B | А ˄ В | А v B |
0 | 1 | 0 | |||
1 | 0 | 1 | |||
1 | 0 | 1 | 0 | ||
0 | 1 | ||||
Task 1. Put the order of operations in correct sequence when calculating the expression: а) ¬
Task 1. Put the order of operations in correct sequence when calculating the expression:
а) ¬ A ˅ (В ˅ ¬ С)
б) А ˅ В ˄ С
в) А ˄ ¬ (В ˅ ¬ С) ˅ D
1
2
4
3
5
1
1
2
2
3
4
Work in pairs
Task 2. Specify the values of variables
Task 2. Specify the values of variables A and B, if:
а) А ˄ В = 1 А = _____ В = _____
Answer: А = 1, В = 1
б) А ˅ В = 0 А = _____ В = _____
Answer: А = 0, В = 0
в) ¬ (А ˄ В) = 1 А = _____ В = _____
Answer: А = 1, В = 0
Work in pairs
Algorithm for constructing the truth table 1
Algorithm for constructing the truth table
1. Determine the number of sets of input variables - all possible combinations of the values of variables included in expressions, using the formula : Q=2n , where n is the number of input variables. It determines the number of rows of the table..
2. Write all input variable sets to the table..
3. Determine the number of logical operations and the sequence of their execution.
4. Fill columns with the results of performing logical operations in the indicated sequence
Task 3. Fill in the truth table of a logical expression: ¬ (А ˄
Task 3. Fill in the truth table of a logical expression:
¬ (А ˄ В)
А | В | А ˄ В | ¬ (А ˄ В) |
Work in pairs / individually
А В С ¬ В А ˅ ¬ В А ˅ ¬ В ˅ С
А | В | С | ¬ В | А ˅ ¬ В | А ˅ ¬ В ˅ С |
Task 4. Fill in the truth table of a logical expression:
А ˅ ¬ В ˅ С
Work in pairs / individually
Work in pairs Find the meaning of expressions : 1
Work in pairs
Find the meaning of expressions :
1 AND (0 OR NOT 0) =
NOT (0 OR 1) AND 1 =
1*(0+1) = 1
0*1= 0
Individual work Construct truth tables for the following logical expressions and determine the value of the logical expression for the given values of variables
Individual work
Construct truth tables for the following logical expressions and determine the value of the logical expression for the given values of variables
F= А ˅ В ˄ С , if А=1, В=1, С=1
F= (А ˅ В ˄ С), if А=0, В=1, С=1
F= (A v B) ˄ (A v B), if А=1, В=0, С=1
F= (А ˅ В) ˄ (С v В), if А=0, В=1, С=0
F= (A ˄ B ˄ C), if А=0, В=0, С=1
In pairs, explain to your partner one thing that you have understood really well
In pairs, explain to your partner one thing that you have understood really well.
Then ask them a question about one thing you would like an answer to.
Can you answer your partner’s question?
Plenary
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