Logic and sets

1003055612

Level:

Find the intersection

A \cap B^{'}

A = (- 4; + \infty)

and

B = (- \infty; 6)

. (By

B^{'}

the complement of the set

B

is denoted.)

[6; + \infty)

(- 4; 6)

[- 4; 6]

(- \infty; 4]

1003055611

Level:

Let

A = (- 1; 5]

and

B = [- 1; 7)

. Give the union

A \cup B

[- 1; 7)

(- 1; 7)

(- 1; 5)

[- 1; 5]

1003055610

Level:

Let

A = (- 3; 5]

and

B = [- 1; + \infty)

. Find the intersection

A \cap B

[- 1; 5]

(- 1; 5)

(- 3; + \infty)

(- 1; 5]

1003055609

Level:

Determine the truth value of the statement

\exists k \in Z : k^{2} < 0

It is a false statement.

It is a true statement.

It is not a statement.

It is impossible to determine whether it is a true or a false statement.

1003055608

Level:

Determine the truth value of the statement

\forall x \in R : x^{2} + 1 > 0

It is a true statement.

It is a false statement.

It is not a statement.

It is impossible to determine whether it is a true or a false statement.

1003055607

Level:

Find a false statement.

(5 < - 10) \lor (4 < 3)

(3 \in N) \Leftrightarrow (3 \in Z)

(2 > 0) \lor (3 = 5)

(8^{2} = 16) \Rightarrow (8^{2} = 15)

1003055606

Level:

Identify a true proposition.

(2 < 5) \land (4 < 5)

(0 < - 1) \lor (8 > 10)

(3 < 5) \Rightarrow (8 \leq - 10)

(5 < 10) \Leftrightarrow (8 \div 3 = 5)

1003055605

Level:

Which of the following expressions is a proposition?

5^{2} = 25

10^{2}

(a - b)^{2} - (a + b)^{2}

Is it raining today?

1003055604

Level:

Let

A = {0; 1; 2; 3}

B = {0; 1; 2}

and

C = {x : x = 3 k + l}

, where

k \in A

l \in B

. Which of the following sets specifies

C

by the list of all its elements?

{0; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11}

{4; 5; 6; 7; 8; 9; 10; 11}

[0; 11]

{0; 1; 2; 3}

1003055603

Level:

Find the set difference

A ∖ B

for

A = {x \in Z : x^{2} = 4}

and

B = {- 1; 0; 1; 2; 3}

{- 2}

{- 1; 0; 1; 3}

{- 2; 2}

{- 2; - 1; 0; 1; 2; 3}

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