Higher mathematics test VK2

Task 24

Question 1. Among the presented pairs of sets, find the equal ones:

1) {1,3, 5, 7, 9} and (9, 7, 5, 3, 1};

2) {@, #, $,%, &,} and {@, #, $,%, №};

3) {x + 2 = 1 | x N} and {x + 2 = 1 | xeR};

4) {articles that make up the Constitution of the Russian Federation} and {articles that make up the Civil Code of the Russian Federation};

5) all presented sets are different.

Question 2. A - the set of natural numbers divisible by 2, B - the set of natural numbers divisible by 3, C - the set of natural numbers divisible by 6. Indicate the correct inclusions:

1) A B, B C;

2) B A, B C;

3) A C, B C;

4) C A, C B;

5) C A, B A.

Question 3. The set A is given by the characteristic condition: A = {x + 2 = 1 | x N}. What is it like?

1) bounded from above;

2) limited from below;

3) empty;

4) non-empty;

5) infinite.

Question 4. The set M is given by the characteristic property: "to be an even number." Find a false statement

1) M = {2n; n N};

2) | M | =;

3) M N;

4) A M; where A = {4n; n N};

5) M = W.

Question 5. The set M is given by the characteristic property: "to be an even number." Find the property that does not match the given set:

1) M is infinite;

2) M is limited from below;

3) M is bounded from above;

4) M is ordered;

5) M is not empty.



Task 25

Question 1. Finish the definition: "A non-empty set is a set whose cardinality ...". Please choose the most complete answer.

1) = 0,

twenty,

3) =,

four) ,

5) = 10.

Question 2. Complete the definition: "An infinite set is a set whose cardinality ..." Choose the most complete answer

1) = 0,

twenty,

3) =,

4) ,

5) = 10.

Question 3. Finish the definition: "A finite set is a set whose cardinality ...".

1) = 0,

twenty,

3) =,

four) ,

5) = 10.

Question 4. Find a subset of the set {10,20,30 ... 100}.

1) {10, 11, 12, ... 99,100},

2) {10,30,50,70,90},

3) {1,2,3 .... 10},

4) {10x | x {0,1,2, ... 10}},

5) Answers 2 and 4 are correct.

Question 5. Find the properties of the set of rational numbers Q.

1) of course, limited, closed with respect to addition;

2) infinite, limited, closed with respect to subtraction;

3) of course, bounded from below, not closed with respect to division;

4) infinite, unlimited, non-closed relative to multiplication;

5) is infinite, unlimited, closed with respect to addition, subtraction, multiplication and division.



Task 26

Question 1. A is the set of roots of the equation Zx2 - 12x - 15 = 0, and B is the set of roots of the equation x2 - 3x - 10 = 0. Find A B.

1) {-2, -1, 5};

2) {5,-1, 5,-2};

3) {5};

4) {-1.-2};

5) {-1}.

Question 2. A is the set of numbers multiples of 7, B is the set of multiples of 3, C is the set of multiples of 2. Describe the set (AB) \ C.

1) these are numbers multiples of 7;

2) these are numbers multiples of 3;

3) these are numbers multiples of 2;

4) these are numbers multiples of 21;

5) these are multiples of 42.

Question 3. A is the set of roots of the equation Zx2 - 12x -15 = 0, and B is the set of roots of the equation x2 - Zx - 10 = 0. Find A \ B.

1) {-2, -1,5};

2) {5, -1,5, -2};

3) {5};

4) {-1.-2};

5) {-1}.

Question 4. Find sets A and B such that 5 A B, 7 A B.

1) A - a set of multiples of 5, B - a set of divisors of 20;

2) A = {4, 5, 6, 7, 8}, B = {1,2, 3,4, 5};

3) A = {x5 | xN}, B = {x; 5 | xN};

4) A is the set of solutions to the equation x2 - 12x + 35 = 0, B is the set of solutions to the equation x2 - 8x + 15 = 0

5) all answers are correct.

Question 5. The set X = {A; IN; FROM; O}, and the set Y = {C; IN; E; H}. Perform action (X \ Y) U (Y \ X).

1) {A; IN; FROM; D; E; H};

2) {A; IN; E; H};

3) {D; FROM};

4) W;

5) there is no correct answer.



Task 27

Question 1. There is a known Cartesian product X x T = {(M, A), (K, B), (M, B), (K, A)}. Define sets A and B.

1) X = {A, B}; T = {M, K};

2) X = {M, K}; T = {A, B};

3) X = {A, A, B, B}; T = {M, K, M, K};

4) X = {M, K, M, K}; T = {A, B, B, A};

5) there is no right answer.

Question 2. n (A) = 7, A x B = W. What is n (B)?

1) 7;

2) 0;

3) 1;

4) 49

5)