1003055606
Level:
B
Identify a true proposition.
\( (2 < 5)\wedge(4 < 5) \)
\( (0 < -1)\vee (8 >10) \)
\( (3 < 5) \Rightarrow (8\leq -10) \)
\( (5 < 10) \Leftrightarrow ( 8\div3=5) \)
Logic and sets
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?
1003055604
Level:
A
Let \( A=\{0;1;2;3\} \), \( B=\{0;1;2\} \) and \( C=\{x\colon x=3k+l\} \), 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:
A
Find the set difference \( A\setminus B \) for \( A=\left\{x\in \mathbb{Z}\colon x^2=4\right\} \) and \( B=\{-1;0;1;2;3\} \).
\( \{-2\} \)
\( \{-1;0;1;3\} \)
\( \{-2;2\} \)
\( \{-2;-1;0;1;2;3\} \)
1003055602
Level:
A
Give the set difference \( A\setminus B \) for \( A = [ -5;7 ] \), \( B=\{7;11\} \).
\( [ -5;7 ) \)
\( [ -5;11) \)
\( [ -5;7 )\cup(7;11) \)
\( [ -5;7 )\cup\{11\} \)
1003055601
Level:
A
Given the sets \( A=[ -12;12 ] \) and \( B=(3;20) \) find the set difference \( A\setminus B \).
\( [ -12;3 ] \)
\( ( -12;3 ] \)
\( [ -12;3 ) \)
\( ( 12;20 ) \)
1103055714
Level:
A
In the diagram below yellow colour represents
the difference of sets \( A \) and \( B \)
the intersection of sets \( A \) and \( B \)
the difference of sets \( B \) and \( A \)
the union of sets \( A \) and \( B \)
1003055713
Level:
A
Choose the correct expression.
\( \{d\}\cup \{d\}\cup \{d\} = \{d\} \)
\( \{d\}\cup \{d\}\cup \{d\} = \{ddd\} \)
\( \{d\}\cup \{d\}\cup \{d\} = \{d;d\} \)
\( \{d\}\cup \{d\}\cup \{d\} = \{d;d;d\} \)
1003055712
Level:
A
The set \( A \) is the set of all divisors of \( 12 \), the set \( B \) is the set of all divisors of \( 6 \). Which relation is correct?
\( B\subset A\)
\( A\subset B\)
\( A=B \)
\( A\cup B=\{1;2;3;6;12\} \)
1003055711
Level:
A
Determine the set of all common divisors of numbers \( 24 \) and \( 18 \).
\( \{ 1;2;3;6 \} \)
\( \{ 1;2;3;4;6;8;9;12;18;24 \} \)
\( \{ 2;3;6 \} \)
\( \{ 1;2;3;4;6;9;12 \} \)