Test work "elements of algebra of logic" of the section "mathematical foundations of computer science". Material for preparation for the Unified State Exam (GIA) in computer science and ICT (grade 9) on topic: A2

Topic “Fundamentals of Logic”

Option – 4

1) For what number X is the statement true? (X>2) (X > 5)→(X< 3)

1) 5 2) 2 3) 3 4) 4

2) For which symbolic expression is the statement false:

First letter is vowel → ¬ (Third letter is consonant)?

1)abedc 2)becde 3)babas 4)abcab

3) What logical expression is equivalent to the expression ¬(A ¬B)?

1) A B 2) A B 3) ¬A ¬B 4) ¬A B

4) What logical expression is equivalent to the expression A  ¬(¬ B  ¬ C) ?

1) A B C 2) A B ¬C 3) A (B C) 4) (A ¬B) ¬C

5

1) ¬X ¬Y Z2) ¬X ¬Y Z

3) X Y ¬Z4) X Y Z

6

1) ¬(X Y) Z2) ¬(X ¬Y) Z

3) ¬(X Y) Z4) (X Y) Z

7) What is the smallest natural number X for which the statement

¬(X· X < 9) → (X >(X + 2))

will be false?

8) How many different solutions does the equation have?

(K L M) (¬L ¬M N) = 1

9) Alyosha, Vitya and Igor found a small weight on the floor in the physics classroom after school. Each of them, examining the find, made two assumptions. Alyosha said: “This is a weight made of brass, and it most likely weighs 5 g.” Vitya suggested that the weight was made of copper and weighed 3 g. Igor believed that the weight was not made of brass and its weight was 4 g. Teacher The physicist was glad that the loss had been found, and told the guys that each of them was only half right. What metal - brass (L) or copper (M) - is the weight made of, and what is its weight? In your answer, write down the first letter of the name of the metal, and then the number corresponding to the weight of the weight, for example, L4.

10) For which name is the statement true:

¬ (Second letter vowel → First letter vowel) Is the last letter a consonant?

1) IRINA 2) MAXIM 3) MARIA 4) STEPAN

11) What logical expression is equivalent to the expression ¬A ¬(¬B ¬¬C) D?

1) ¬A ¬B C D2) ¬A ¬B ¬C D

3) ¬A B ¬C D 4) ¬A B C D

12) On one street there are 4 houses in a row, in which 4 people live: Alexey, Egor, Victor and Mikhail. It is known that each of them has exactly one of the following professions: Turner, Carpenter, Surgeon and Oculist, but it is unknown who is which and it is unknown who lives in which house. However, it is known that:

(1) The Turner lives to the left of the Joiner

(2) The surgeon lives to the right of the Oculist

(3) The ophthalmologist lives next to the Joiner

(4) The Turner does not live next to the Joiner

(5) Victor lives to the right of the Oculist

(6) Mikhail is not a Turner

(7) Egor lives next to Stolyar

(8) Victor lives to the left of Yegor

Find out who has what profession and who lives where, and give the answer in capital letters of the people's names, in order from left to right. For example, if (from left to right) Konstantin, Nikolai, Roman and Oleg lived in the houses, the answer would be: KNRO.

13) How many different solutions does the equation have?

(K L) (M N) = 1

where K, L, M, N are logical variables? The answer does not need to list all the different sets of values ​​of K, L, M and N for which this equality holds. As an answer, you only need to indicate the number of such sets.

14) It is known that for the numbers X, Y and Z the statement is true

(Z< X  Z< Y)  ¬(Z+1< X)  ¬(Z+1< Y)

What is the value of Z if X=25 and Y=48?

15) For which character set is the statement true:

Second letter consonant (The word has 3 vowels Is the first letter a consonant)?

1) UBBOSHT 2) TUIOSHSH 3) SHUBVOI 4) ITTRAO

16) When the computer broke down, its owner said, “The memory could not fail.” His son suggested that the processor had burned out, but the hard drive was working. The service technician who came said that, most likely, everything was fine with the processor, but the memory was faulty. As a result, it turned out that two of them said everything correctly, and the third said everything wrong. What's broken?

17) What is the largest positive integer X for which the following statement is true:

(X (X+1) > X X + 7) → (X (X+1) ≤ X X + 7)

¬ - sign denoting negation

Preparation for the State Examination in 9th grade in computer science and ICT

Logical values, operations, expressions

Demo version of GIA 2012

For which of the given names true saying:

NOT (First letter is vowel) AND NOT (Last letter is consonant)?

1) Emelya 2) Ivan 3) Mikhail 4) Nikita

Solution:

NOT (First letter is vowel) AND NOT (Last letter is consonant),

MIOO, 2011 option 1

NOT (First letter is vowel) AND (Last letter is vowel),

MIOO, 2011 option 2

NOT(First letter is vowel) OR (Last letter is vowel),

For which character set is the statement FALSE:

The first letter is a consonant  The fourth letter is a consonant?

1) Masha

2) Artem

3) Plato

4) Anastasia

For what name FALSE saying:

The first letter is a vowel  The fourth letter is a consonant?

• Peter

• Alexey

• Natalia

• Elena

Which of the following animal names satisfies the logical condition:

Are there five letters in the word & Is the fourth letter a vowel?

A) Zebra B) Elephant C) Wild boar D) Deer

For which character set is the following statement TRUE?

The second letter is a consonant  (There are 3 vowel letters in a word  The first letter is a consonant)?

1) ABBEJK

2) KAIEZHJ

3) TOAD

4) ICCROE

For which of the following words TRUE logical expression

NOT (the first letter is a vowel) AND NOT (the third letter is a consonant)?

• Modem

• Address

• Channel

• Connection

For which character set? FALSE saying:

First letter is vowel → ¬(Third letter is consonant)?

A) IKANM B) KAINA C) KIKIS D) IKMIK

Which of the given names satisfies the condition:

(Second letter is vowel  First letter is vowel) last letter is consonant?

1) Alexey

2) Pavel

3) Ksenia

4) Marina

Which of the given names satisfies the condition:

(First letter is vowel  First letter is consonant) Second letter is consonant

• Irina

• Kirill

• Galina

• Sergey

For which animal name is the statement FALSE:

Ends with a consonant  There are 7 letters in the word  ┐(The third letter is a consonant)?

1) Ostrich

2) Leopard

3) Camel

4) Kangaroo

Demo version of GIA 2012

How many records in this fragment satisfy the condition

(Precipitation = "rain") OR (Pressure

In your answer, indicate one number - the required number of records.

Answer: ___________________________.

(Precipitation = "rain") OR (Pressure

Answer: 5

(Part of the world = “Asia”) AND (Altitude >5000)?

Answer: 3

(Part of the world = “Europe”) OR (Altitude

Answer: 4

Below in tabular form is a fragment of the database on student testing results (a hundred-point scale is used):

“Place 4 OR M3>12)”?

Answer: 4

The second way to solve such a problem is “Place 4 OR M3>12)”

The conjunction takes on the meaning TRUE only in one case, if both statements take on meaning TRUE.

Based on this, we check the condition in brackets in the first five lines, since ( Place)

How many entries in the following fragment of the tournament table satisfy the condition

How many entries in the following fragment of the tournament table satisfy the condition

« Place 2 OR O>6)»?

« Place 2 OR O>6)»?

« Place 2 OR O>6)»?

Sources of information

• “Informatics and ICT. Profile level": Methodological manual / I.G. Semakin, T.Yu. Sheina. – M.: BINOM. Knowledge Laboratory, 2010.

• “Unified State Exam 2010. Computer Science. Typical test tasks / P.A. Yakushkin, V.R. Leshchiner, D.P. Kiriyenko." – M.: Publishing House “Exam”, 2011

• Informatics: Textbook. Manual for 10-11 grades. general education Institutions / L.Z. Shautsukova. – M.: Education, 2003.

• mytest.klyaksa.net

• Demo versions of the Unified State Exam 2009, 2010, 2011

• Computer Science and ICT. 9th grade. Preparation for State Examination 2011/Edited by F.F. Lysenko, L.N. Evich. – Rostov-on-Don: Legion-M, 2011. – 272 p. – (GIA-9)

• Informatics: GIA: Educational and reference materials for grade 9 (Series “Final control: GIA”)/ S. M. Avdoshin, R. 3. Akhmetsafina, O. V. Maksimenkova, I. N. Lesovskaya, M. V. Kurak, N. P. Lipkin, S. A. Semikina. - M.; St. Petersburg: Education, 2011.- 252 p.: ill.

OGE - 2 (A) Part 1, basic level, the task involves selecting and writing an answer in the form of one number, completion time - 3 minutes, maximum score for completing the task - 1. Requirements for the level of training, the mastery of which is tested during the exam when answering this task: complete the basic operations on objects: strings of characters, numbers, lists, trees; check the properties of these objects; execute and build simple algorithms;

What you need to know

Theoretical information

Algebra of logic is a mathematical apparatus with the help of which logical statements are written, calculated, simplified and transformed.

Statements are divided into three types: general, private or single. The general statement begins with the words: All, any, every, none. A private statement begins with the words: some, majority etc. in all other cases the utterance is singular.

Logical statement is a declarative sentence about which we can definitely say: it is true (1) or false (0).

Composite(complex) statements are constructed from simple ones using basic logical connectives (operations) “and”, “or”, “not”.

Operation priority:

1. Expression in parentheses
2. Inversion
3. Conjunction
4. Disjunction
5. Implication
6. Equivalence

For additional study of the topic, you can use the material by Natalya Vladimirovna Shabaldina: basics of logic.pptx

Example assignment

For which of the animal names is the following statement false?
A word has 4 vowels and no (the fifth letter is a vowel) or a word has 5 consonants?
1) Chinchilla 2) Kangaroo 3) Antelope 4) Crocodile

Solution:

Let us introduce the following notation:
A= "The word has 4 vowels";
IN= "fifth letter vowel";
WITH= "there are 5 consonants in the word."
Let's create a logical expression: A and not B or C.
Let's determine the procedure and fill out the table:

From the truth table it is clear that the statement is false only for the word "Kangaroo".
Answer: 2

Tasks for training

1. For which of the indicated values ​​of the number X is the expression false?
   (X > 2) OR NOT (X > 1)?

1. 
   (X< 3) И ((X < 2) ИЛИ (Х > 2))?

1. For which of the indicated values ​​of the number X is the expression true?
   (X > 4) OR (X< 7) И (Х < 6 )?

8. For which of the given numbers is the following statement true:

NOT (First digit is even) AND NOT (Second digit is odd)?

¬ ( The first letter of the name is a vowel → The fourth letter of the name is a consonant)?

1) ELENA 2) VADIM 3) ANTON 4) FEDOR

1. For which symbolic expression is the statement false:

First letter is vowel → ¬ (Third letter consonant)?

1) abedc 2) becde 3) babas 4) abcab

1. For which character set is the statement true:

Second letter consonant ^ (The word has 3 vowels v The first letter is a consonant )?

1) UBBOSHT 2) TUIOSHSH 3) SHUBVOI 4) ITTRAO

1. For which name is the statement false:

(First letter is vowel^ The last letter is a consonant) → ¬ (The third letter is a consonant) ?

1) DMITRY 2) ANTON 3) EKATERINA 4) ANATOLY

1. For which name is the statement true:

First letter is vowel ^ Fourth letter consonant v The word has four letters ?

1) Sergey 2) Vadim 3) Anton 4) Ilya

1. For which name is the statement true:

(First letter consonant → Second letter vowel) ^ The last letter is a consonant ?

1. For which name is the statement true:

(Second letter vowel → First letter is vowel) ^ The last letter is a consonant ?

1) ALICE 2) MAXIM 3) STEPAN 4) ELENA

1. For which river name is the statement false:

(Second letter vowel → Penultimate letter consonant) ^ The first letter comes before the third in the alphabet ?

1) DANUBE 2) MOSCOW 3) DVINA 4) VOLGA

18) For which of the indicated values ​​of the number X is the expression true? (X<3) & ((X <2) V (X>2) )?

20) For which of the indicated values ​​of the number X is the expression true? (X>1) & (X>2) & (X≠3)?

21) For what number is the statement true? ((X > 3)v(X < 3)) → (X < 1)

1) 1 2) 2 3) 3 4) 4

22) For what number is the statement true ( X > 1) ^ ((X < 5) → (X < 3))

1) 1 2) 2 3) 3 4) 4

Literature:

1. codifier of content elements and requirements for the level of training of students for the main state exam in COMPUTER SCIENCE, 2015 - 2019;
2. specification of control measuring materials for conducting the main state exam in INFORMATION SCIENCE and ICT in 2015 - 2019;
3. open bank of tasks in computer science and ICT: http://oge.fipi.ru/os/xmodules/qprint/index.php?proj=74676951F093A0754D74F2D6E7955F06 .