1103055614
Level:
A
Determine which of the following conditions for \( x \) defines the same set as is defined by the given diagram.
\( x\in(-3;1] \)
\( x\in[-3;1) \)
\( -3\leq x\leq1 \)
\( x \leq 1 \) or \(x\geq -3\)
Logic and sets
1003055613
Level:
A
Give the intersection \( A\cap B \) if \( A=[-7;1] \) and \( B=(1;2) \).
\( \emptyset \)
\( \{1\} \)
\( [-7;2) \)
\( (-7;2) \)
1003055612
Level:
A
Find the intersection \( A\cap B' \) if \( A=(-4;+\infty) \) and \(B=(-\infty;6) \). (By \(B'\) the complement of the set \( B \) is denoted.)
\( [ 6;+\infty) \)
\( (-4;6) \)
\( [-4;6] \)
\( (-\infty;4] \)
1003055611
Level:
A
Let \( A=(-1;5] \) and \( B=[ -1;7) \). Give the union \( A\cup B\).
\( [ -1;7 ) \)
\( ( -1;7 ) \)
\( ( -1;5 ) \)
\( [ -1;5] \)
1003055610
Level:
A
Let \( A=(-3;5] \) and \( B=[-1;+\infty) \). Find the intersection \( A\cap B \).
\( [ -1;5] \)
\( (-1;5) \)
\( (-3;+\infty) \)
\( (-1;5] \)
1003055609
Level:
B
Determine the truth value of the statement \( \exists k\in\mathbb{Z}\colon k^2 < 0\).
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:
B
Determine the truth value of the statement \( \forall x\in\mathbb{R}\colon x^2+1>0 \).
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:
B
Find a false statement.
\( (5 < -10) \vee (4 < 3) \)
\( (3\in\mathbb{N})\Leftrightarrow (3\in\mathbb{Z} ) \)
\( (2 > 0)\vee(3=5) \)
\( \left(8^2 = 16 \right) \Rightarrow \left(8^2 = 15 \right) \)
1003055606
Level:
B
Identify a true proposition.
\( (2 < 5)\wedge(4 < 5) \)
\( (0 < -1)\vee (8 >10) \)
\( (3 < 5) \Rightarrow (8\leq -10) \)
\( (5 < 10) \Leftrightarrow ( 8\div3=5) \)
1003055605
Level:
B
Which of the following expressions is a proposition?
\( 5^2=25 \)
\( 10^2 \)
\( (a-b)^2 - (a+b)^2 \)
Is it raining today?