Logic and Sets

1003055705

Level:

Given the sets \begin{gather*} A = \{1, 2, 3, 4, 5, 6, 7, 8, 9\},\\ B = \{3, 4, 5, 6, 7\},\\ C = \{6, 7, 8, 9, 10, 11, 12\}, \end{gather*} find the union \( A\cup B\cup C \).

\( \{1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12\} \)

\( \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \)

\( \{6, 7\} \)

\( \{1, 2, 10, 11, 12\} \)

1003055706

Level:

Given the sets \begin{gather*} A = \{ 3, 4, 5, 6, 7, 8\},\\ B = \{3, 4, 5, 6, 7\},\\ C = \{6, 7, 8, 9, 10,11\}, \end{gather*} find the intersection \( A\cap B\cap C \).

\( \{ 6, 7\} \)

\( \{3, 4, 5, 6, 7, 8, 9, 10, 11\} \)

\( \{3, 4, 5, 6, 7\} \)

\( \{9, 10, 11\} \)

1003055707

Level:

Let \( A = \{a, b, c, d, e, f\} \), \( B = \{a, k, b, l\} \). Find the union \( A\cup B \).

\( \{a, b, c, d, e, f, k, l\} \)

\( \{a, b\} \)

\( \{ c, d, e, f\} \)

\( \{k, l\} \)

1003055708

Level:

Let \( A = \{a, b, c, d, e, f\} \), \( B = \{a, g, b, h, i\} \). Determine the intersection \( A\cap B\).

\( \{a, b\} \)

\( \{a, b, c, d, e, f, g, h, i\} \)

\( \{ g, h, i\} \)

\( \{c, d, e, f\} \)

1003055709

Level:

Give the intersection \( A\cap B \) if \( A=\{1, 3, 5, 7, 9\} \) and \( B=\{0, 3, 6, 9\} \).

\( \{3, 9\} \)

\( \{0, 1, 3, 5, 6, 7, 9\} \)

\( \{1, 5, 7\} \)

\( \{0, 6\} \)

1003055710

Level:

Give the difference of sets \( A \) and \( B \) if \( A = \{4, 5, 6\}\) and \(B = \{5, 6, 7\} \).

\( \{4\} \)

\( \{7\} \)

\( \{4, 5, 6, 7\} \)

\( [ 4,5 ] \)

1003055711

Level:

Determine the set of all common divisors of numbers \( 24 \) and \( 18 \).

\( \{ 1,2,3,6 \} \)

\( \{ 1,2,3,4,6,8,9,12,18,24 \} \)

\( \{ 2,3,6 \} \)

\( \{ 1,2,3,4,6,9,12 \} \)

1003055712

Level:

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?

\( B\subset A\)

\( A\subset B\)

\( A=B \)

\( A\cup B=\{1,2,3,6,12\} \)

1003055713

Level:

Choose the correct expression.

\( \{d\}\cup \{d\}\cup \{d\} = \{d\} \)

\( \{d\}\cup \{d\}\cup \{d\} = \{ddd\} \)

\( \{d\}\cup \{d\}\cup \{d\} = \{d,d\} \)

\( \{d\}\cup \{d\}\cup \{d\} = \{d,d,d\} \)

1103055614

Level:

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 \(x\geq -3\)

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