1003034302
Level:
B
Given the sets \( A=(-6,2] \), \( B=[-2,8) \) and \( C=(0,3] \), determine \( (A\cap B)\setminus C \).
\( [-2,0] \)
\( [-2,0) \)
\( [-6,8) \)
\( (-6,0)\cup(3,8) \)
Logic and Sets
1003034301
Level:
B
Given the sets \( A=(-1,+\infty) \) and \( B=[-3,6) \), find the intersection \( A'\cap B \).
\( [-3,-1] \)
\( [-1,6) \)
\( [-3,-1) \)
\( (-3,-1) \)
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 \(x\geq -3\)
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.
\( (5 < -10) \vee (4 < 3) \)
\( (3\in\mathbb{N})\Leftrightarrow (3\in\mathbb{Z} ) \)
\( (2 > 0)\vee(3=5) \)
\( \left(8^2 = 16 \right) \Rightarrow \left(8^2 = 15 \right) \)