Logic and sets

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?

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)

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)

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.

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.

1103055701

Level:

Which diagram represents the interval that is the set of all solutions of the inequality

- 4 < x + 1 < 4

2010000601

Level:

Given the sets

A = {x \in Z : x > - 1}

and

B = {x \in N : x \leq 3}

find the intersection

A \cap B

{1; 2; 3}

{0; 1; 2; 3}

{1; 2}

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

2010001401

Level:

Given the sets

A = Z

and

B = {x \in N : x < 5}

, find the union

A \cup B

Z

N

\emptyset

{1; 2; 3; 4}

2010001402

Level:

Find the set

(B ∖ A) \cap C

for

A = [- 5; 0)

B = [- 1; 10)

and

C = (- 2; 2]

[0; 2]

(0; 2]

[- 2; - 1)

[- 5; 2]

2010001405

Level:

Find the set difference

A ∖ B

for

A = {x \in Z : | x | < 3}

and

B = {x \in N : x \geq 2}

{- 2; - 1; 0; 1}

\emptyset

{2}

{- 2; - 1; 0}

1003055605

1003055606

1003055607

1003055608

1003055609

1103055701

2010000601

2010001401

2010001402

2010001405

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