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Test work on the topic "Algebra of Logic" (part 1)

Option 1

1.      Solve a logic problem in any way:

The three divisions A, B and C of the trading firm were striving to get profit at the end of the year. Economists have made the following assumptions:

1)     department A will make a profit if and only if making a profit by department C will not be a sufficient basis for making a profit by department B;

2)     division A or division C will not receive profit, or at the same time they will not receive profit;

3)     department A or department C will profit

At the end of the year, only one of the three assumptions turned out to be true. Which divisions made a profit?

2.      How many integer values ​​of X are there for which the statement is false:

 ¬ ((| X | <5) Ù (| X | <1) Ù (| X | <10))

3.      (rated "Excellent") How many different solutions does the system of equations have?

(for "Good") How many different solutions does the equation have?

(((¬K → M) → (M Ù ¬L Ù ¬N)) Ú ((¬K Ù ¬M) → (¬M Ú L Ú N))) Ù (L Ù M) = 1

where J, K, L, M, N are boolean variables?

4.      additional... Solve a logic problem

At the Pedagogical Institute, Arkadyev, Babanov, Korsakov, Dashkov, Ilyin and Flerov teach economic geography, English, German, history, French, and mathematics.

It is known that:

1)     a German teacher and a mathematics teacher in their student years were engaged in rhythmic gymnastics;

2)     Ilyin is older than Flerov, but his work experience is less than that of a teacher of economic geography;

3)     being students, Arkadieva and Babanova studied together at the same university. All others graduated from the Pedagogical Institute;

4)     Flerov is the son of a French teacher, but he was not a student;

5)     the French teacher is the oldest of all in terms of age and work experience. He has been working at the Pedagogical Institute since he graduated. The teachers of mathematics and history are his former students;

6)     Arkadiev is older than the teacher of the German language;

Who teaches what subject?

Test work on the topic "Algebra of Logic" (part 1)

Option 2

1.      Solve the problem in any way:

At one evening, there were five officers among the guests: an infantryman, an artilleryman, a pilot, a signalman and a sapper. One of them is a captain, three are majors, and one is a colonel. The ladies surrounded the officers with such attention that all the other guests were simply forgotten. From conversations we managed to find out the following:

1)  Peter has the same rank as his friend a sapper;

2)  the communications officer and Nikolai are great friends;

3)  the pilot-officer, along with Vladimir and Alexander, were recently visiting Nikolai;

4)  shortly before the party, the artilleryman and the sapper had their radios out of order almost simultaneously. Both turned to Alexander with a request to visit them and help the signalman fix the malfunction, and since then the receivers for both have worked perfectly;

5)  Nikolai almost became a pilot, but then, on the advice of his sapper friend, chose a different type of troops;

6)  Peter is older than Alexander in rank, and Vladimir is older than Nikolai;

7)  Andrey was visiting Alexander on the eve of the party.

Determine the rank of each officer and the type of service in which he serves.

2.      Make a truth table for a logic function

X = (¬A → B) Ù (B ↔ (¬C → A))

in which the column of the values ​​of the argument A = 236, B = 132, C = 17. Convert the resulting binary notation of the values ​​of the function X to the decimal number system.

3.      (rated "Excellent") Solve the system of logical equations. Determine the number of solutions:

(for "Good") How many different solutions does the equation have?

¬ ((J → K) → (M Ù N)) Ú ¬ ((M Ù N) → (¬J Ú K)) Ú (M Ù N Ù K Ù L) = 0

where J, K, L, M, N are boolean variables?

4.      additional... Solve the logic problem:

Last night:

1)     Andrey went to the concert; 2) Boris spent all the time with Olga;

3) Eugene never saw Rosa; 4) Polina went to the cinema;

5) Rose watched the play in the theater; 6) a couple attended an art exhibition.

In addition, whom we have already named, Dmitry and Serafima were constantly members of the same company. Together with each young man there was a girl. All the couples were in different places. Who was with whom and where?