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?
Logic and sets
1003055606
Level:
B
Identify a true proposition.
\( (2 < 5)\wedge(4 < 5) \)
\( (0 < -1)\vee (8 >10) \)
\( (3 < 5) \Rightarrow (8\leq -10) \)
\( (5 < 10) \Leftrightarrow ( 8\div3=5) \)
1003055607
Level:
B
Find a false statement.
\( (5 < -10) \vee (4 < 3) \)
\( (3\in\mathbb{N})\Leftrightarrow (3\in\mathbb{Z} ) \)
\( (2 > 0)\vee(3=5) \)
\( \left(8^2 = 16 \right) \Rightarrow \left(8^2 = 15 \right) \)
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.
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.
1103055701
Level:
B
Which diagram represents the interval that is the set of all solutions of the inequality \( -4 < x+1< 4 \).
2010000601
Level:
B
Given the sets \(A = \{x\in \mathbb{Z}:x> - 1\}\)
and \(B = \{x\in \mathbb{N}: x\leq 3\}\) find the intersection \(A \cap B\).
\(\{1;2;3\}\)
\(\{0;1;2;3\}\)
\(\{1;2\}\)
\(\{-2;-1;0;1;2;3\}\)
2010001401
Level:
B
Given the sets \(A =\mathbb{Z}\)
and \(B = \{x\in \mathbb{N}\ \colon x < 5\}\),
find the union \(A\cup B\).
\(\mathbb{Z}\)
\(\mathbb{N}\)
\(\emptyset \)
\( \{ 1;2;3;4\}\)
2010001402
Level:
B
Find the set \( (B\setminus A) \cap C \) for \( A=[ -5;0) \), \( B=[ -1;10) \) and \( C=(-2;2 ] \).
\( [ 0;2]\)
\( ( 0;2]\)
\( [ -2;-1)\)
\( [ -5;2]\)
2010001405
Level:
B
Find the set difference \(A\setminus B\)
for \(A = \{x\in \mathbb{Z}\ \colon \left |x\right | < 3\}\)
and \(B = \{x\in \mathbb{N}\ \colon x \geq 2\}\).
\(\{ - 2;-1;0;1\}\)
\( \emptyset \)
\(\{ 2\}\)
\(\{ - 2;-1;0\}\)