Exercises with set operations (Batch 2)
Compute the set described by the formula below.
\[ (\{c\} \cap \{d, b\}) \cup (\{d, b\} - \{f, a, c\}) \]
\[ \{d, b\} \]
Compute the set described by the formula below.
\[ (\{a, b\} \cup (\{d, a, b, c\} - \{a, b\})) \cup (\{a, b\} \cap \{d, a, b, c\}) \]
\[ \{a, b, c, d\} \]
Compute the set described by the formula below.
\[ \{b\} \cup (\{b\} \cup (\{f\} \cap \{b\})) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ (\{b\} - \{a\}) \cup (\{b\} - \{d, f, a, e\}) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ (\{e\} \cup \{e\}) \cup (\{d, e, b, c\} \cup \{a\}) \]
\[ \{a, b, c, d, e\} \]
Compute the set described by the formula below.
\[ \{f\} \cup (\{f\} - (\{e, a, f\} - \{f\})) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ (\{e, a\} \cap (\{d\} - \{e, a\})) \cap (\{e, a\} \cap \{d\}) \]
\[ \emptyset \]
Compute the set described by the formula below.
\[ (\{c\} \cup \{c\}) - (\{c\} - \{c\}) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ \{f\} - (\{e\} - (\{a\} \cap \{e\})) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ \{d\} - \{b, c\} \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ \{\{\{d, f, a\}, \{\{\{e\}, \{\{\{c\}\}, \{c\}\}\}, \{e\}\}, \{b\}\}, \{\{\{e\}, \{\{\{c\}\}, \{c\}\}\}, \{e\}\}\} \cap (\{\{\{d, f, a\}, \{\{\{e\}, \{\{\{c\}\}, \{c\}\}\}, \{e\}\}, \{b\}\}, \{\{\{e\}, \{\{\{c\}\}, \{c\}\}\}, \{e\}\}\} \cap (\{\{\{d, f, a\}, \{\{\{e\}, \{\{\{c\}\}, \{c\}\}\}, \{e\}\}, \{b\}\}, \{\{\{e\}, \{\{\{c\}\}, \{c\}\}\}, \{e\}\}\} - \{b, c\})) \]
\[ \{\{\{d, f, a\}, \{\{\{e\}, \{\{\{c\}\}, \{c\}\}\}, \{e\}\}, \{b\}\}, \{\{\{e\}, \{\{\{c\}\}, \{c\}\}\}, \{e\}\}\} \]
Compute the set described by the formula below.
\[ (\{c\} - (\{e\} - \{c\})) \cup (\{e\} \cup \{c\}) \]
\[ \{e, c\} \]
Compute the set described by the formula below.
\[ \{a\} - (\{c\} \cup (\{a\} \cap \{c\})) \]
\[ \{a\} \]
Compute the set described by the formula below.
\[ \{d\} - (\{c\} - (\{d, f\} \cap \{c\})) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ (\{b\} \cap \{b\}) \cup (\{b\} \cup \{b\}) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ \{f, b, c\} \cap (\{f, b, c\} \cup \{e\}) \]
\[ \{f, b, c\} \]
Compute the set described by the formula below.
\[ (\{d, f, b, c\} \cap \{b\}) \cup (\{d, f, b, c\} \cup \{b\}) \]
\[ \{f, b, c, d\} \]
Compute the set described by the formula below.
\[ (\{a\} \cap \{f\}) \cup (\{e\} \cup \{a\}) \]
\[ \{e, a\} \]
Compute the set described by the formula below.
\[ (\{d\} \cup (\{d\} \cap \{d\})) \cup (\{d\} \cap \{d\}) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ (\{d, b, c\} \cap \{d, a\}) \cap (\{d, a\} \cap \{d, b, c\}) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ \{e\} \cup (\{e\} \cap (\{a\} \cap \{e\})) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ (\{d, e, c\} - \{f, a, c\}) \cap (\{f\} \cup \{d, e, c\}) \]
\[ \{d, e\} \]
Compute the set described by the formula below.
\[ \{a\} \cap (\{a, b\} \cup (\{d, f\} \cap \emptyset)) \]
\[ \{a\} \]
Compute the set described by the formula below.
\[ (\{d, f\} \cap \emptyset) \cup (\{b\} - \emptyset) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ (\{\{\emptyset, \{a\}, \{\{f\}, \{\{e\}, \{f\}\}\}\}, \{a\}\} - (\{e, c\} \cap \{\{\emptyset, \{a\}, \{\{f\}, \{\{e\}, \{f\}\}\}\}, \{a\}\})) - (\{e\} \cap \{\{\emptyset, \{a\}, \{\{f\}, \{\{e\}, \{f\}\}\}\}, \{a\}\}) \]
\[ \{\{\emptyset, \{a\}, \{\{f\}, \{\{e\}, \{f\}\}\}\}, \{a\}\} \]
Compute the set described by the formula below.
\[ \{f, a\} - (\{\{\{f\}, \{d, a, b\}\}, \{f\}\} \cap \{e, c\}) \]
\[ \{f, a\} \]
Compute the set described by the formula below.
\[ \{a\} \cup \{b\} \]
\[ \{a, b\} \]
Compute the set described by the formula below.
\[ \{f\} \cup \{d\} \]
\[ \{d, f\} \]
Compute the set described by the formula below.
\[ \{f\} - (\{e\} - (\{a\} \cup \{f\})) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ \{d\} - (\{d\} - (\{d\} - \{f\})) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ (\{a, c\} - (\{a, c\} \cap \{d, b\})) \cap (\{c\} \cup \{d, b\}) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ \{f, e\} - (\{d, e, c\} \cap (\{d\} \cup \{a\})) \]
\[ \{f, e\} \]
Compute the set described by the formula below.
\[ \{c\} - (\{d, f\} \cup (\{d, f\} \cap \{e, c\})) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ (\{d, c\} \cap \{\{c\}, \{\{a\}, \{c\}\}\}) \cup (\{d, c\} \cup \{\{c\}, \{\{a\}, \{c\}\}\}) \]
\[ \{d, \{c\}, \{\{a\}, \{c\}\}, c\} \]
Compute the set described by the formula below.
\[ (\{d\} - \{f\}) \cup (\{c\} \cup \{d\}) \]
\[ \{d, c\} \]
Compute the set described by the formula below.
\[ \{b\} \cup (\{b\} \cap \{e, a, c\}) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ (\{c\} \cap \{f\}) \cup (\{f\} - \{c\}) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ \{f, a, e\} \cup (\{a, c\} \cup (\{b, c\} \cup \{a, c\})) \]
\[ \{f, a, b, c, e\} \]
Compute the set described by the formula below.
\[ \{a, \{e, a\}\} \cup \{f, e, a, c\} \]
\[ \{f, a, c, e, \{e, a\}\} \]
Compute the set described by the formula below.
\[ (\{e\} \cap \emptyset) \cup (\{f\} - \{e\}) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ \{e\} \cap \{f, e\} \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ (\{f\} - \{b\}) \cup (\{f\} \cap \{e\}) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ \{f\} - (\{f\} \cap (\{f\} \cap \{b\})) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ (\{d\} \cup \{e, b\}) \cup (\{\{\{d\}, \{e, b, c\}\}, \{d\}\} \cap \{d, e\}) \]
\[ \{d, e, b\} \]
Compute the set described by the formula below.
\[ \{a\} - (\{f\} \cup (\{f\} \cup \{f\})) \]
\[ \{a\} \]
Compute the set described by the formula below.
\[ \{a\} \cup (\{c\} \cup (\{e, f\} \cap \{c\})) \]
\[ \{a, c\} \]
Compute the set described by the formula below.
\[ \{e, a, c\} - (\{d\} - (\{d, c\} - \{e, a, c\})) \]
\[ \{e, a, c\} \]
Compute the set described by the formula below.
\[ \{e\} - (\{e\} \cap (\{e\} \cap \emptyset)) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ \{d\} \cup \{c\} \]
\[ \{d, c\} \]
Compute the set described by the formula below.
\[ \{c\} - (\{c\} \cap (\{a\} \cap \{e\})) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ \{e, a\} - (\{a\} - (\{a\} \cup \{f, a\})) \]
\[ \{e, a\} \]
Compute the set described by the formula below.
\[ \{e\} \cup \{e\} \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ (\{f\} - \{c\}) \cup (\{c\} - \{f\}) \]
\[ \{f, c\} \]
Compute the set described by the formula below.
\[ (\{e, f, b, c\} \cap (\{a, c\} \cup \{e, f, b, c\})) - (\{e, f, b, c\} \cup \{a, c\}) \]
\[ \emptyset \]
Compute the set described by the formula below.
\[ \{b\} - (\{a\} \cap (\{a\} \cap \{b\})) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ (\{c\} \cup \{f\}) \cup (\{f\} \cup \{a\}) \]
\[ \{f, a, c\} \]
Compute the set described by the formula below.
\[ (\{f, c\} \cup \{a\}) \cup (\{f, c\} \cap \{e\}) \]
\[ \{f, a, c\} \]
Compute the set described by the formula below.
\[ \{c\} - (\{e, b\} \cup (\{f\} \cap \{d, e, f, c\})) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ \{d, e\} \cup (\{d, b\} \cap (\{d, f\} - \{d, e\})) \]
\[ \{d, e\} \]
Compute the set described by the formula below.
\[ \{c\} \cup (\{c\} \cup (\{c\} - \{d, b\})) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ (\{a, b\} \cup (\{b\} \cap \{a, b\})) - (\{a, b\} - \{f, a\}) \]
\[ \{a\} \]
Compute the set described by the formula below.
\[ \{d, a\} - (\{f\} - (\{f, e\} \cap \{b\})) \]
\[ \{d, a\} \]
Compute the set described by the formula below.
\[ \{b\} - (\{c\} \cap (\{c\} \cup \{b\})) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ \{e\} \cup \{a\} \]
\[ \{e, a\} \]
Compute the set described by the formula below.
\[ (\{f\} \cap \{e, a, f\}) \cup (\{e, a, f\} \cup \{f\}) \]
\[ \{f, a, e\} \]
Compute the set described by the formula below.
\[ (\{e\} - \{b\}) \cup (\{e\} - \{b\}) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ \{c\} - (\{c\} \cap (\{a\} \cup \{f\})) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ (\{b\} \cap \{e, a, b, f\}) \cap (\{e, a, b, f\} \cap \{b\}) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ \{a\} \cup (\{a\} \cup (\{a\} \cup \{d, \{e, b, c\}\})) \]
\[ \{d, a, \{e, b, c\}\} \]
Compute the set described by the formula below.
\[ \{e\} \cap (\{e\} \cup (\{d, f\} - \{e\})) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ \{e, b\} \cup (\{e, b\} \cup \{b\}) \]
\[ \{e, b\} \]
Compute the set described by the formula below.
\[ \{f\} - (\{f\} - \{d\}) \]
\[ \emptyset \]
Compute the set described by the formula below.
\[ \{\{\{e\}, \{\{\{d\}, \{\{d\}\}\}, \{e\}\}\}, \{\{f, a\}, \{\{e\}, \{\{\{d\}, \{\{d\}\}\}, \{e\}\}\}\}\} - (\emptyset \cap (\{a\} \cap \emptyset)) \]
\[ \{\{\{f, a\}, \{\{e\}, \{\{\{d\}, \{\{d\}\}\}, \{e\}\}\}\}, \{\{e\}, \{\{\{d\}, \{\{d\}\}\}, \{e\}\}\}\} \]
Compute the set described by the formula below.
\[ \{d, f, b, e\} \cup (\{e, a\} \cup (\{d, f, b, e\} \cup \{e\})) \]
\[ \{d, f, a, b, e\} \]
Compute the set described by the formula below.
\[ \{d, e, a, f\} \cap (\{d, e, a, f\} - \{d, f\}) \]
\[ \{e, a\} \]
Compute the set described by the formula below.
\[ (\{a\} - \{d\}) \cup (\{d\} \cup \{a\}) \]
\[ \{d, a\} \]
Compute the set described by the formula below.
\[ \{d\} - (\{d, c\} - (\{d, c\} \cup \{d\})) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ (\{e\} \cap \{d, a\}) - (\{d, a\} - \{e\}) \]
\[ \emptyset \]
Compute the set described by the formula below.
\[ (\{c\} \cup (\{e, b\} - \{c\})) - (\{e, b\} - \{c\}) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ (\{e\} - (\{f, a\} \cap \{f\})) \cap (\{e\} \cup \{\{d, e\}, \{\{d, e\}, \{c\}\}\}) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ \{e, c\} \cup \{f\} \]
\[ \{e, f, c\} \]
Compute the set described by the formula below.
\[ (\{e, f, c\} \cup \{a\}) \cap (\{a\} \cap \{d, a, b\}) \]
\[ \{a\} \]
Compute the set described by the formula below.
\[ (\{e\} - (\{\{\{d, b\}, \{d, c\}\}, \{d, b\}\} \cup \{d\})) \cup (\{f, a\} \cap \{d\}) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ (\{d, f, b\} \cup \{d\}) - (\{d\} - \{d, f, b\}) \]
\[ \{d, f, b\} \]
Compute the set described by the formula below.
\[ (\{f\} \cup (\{f\} - \{e, a\})) - (\{f\} \cap \{e, a\}) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ \{d\} \cup (\{c\} - \{d\}) \]
\[ \{d, c\} \]
Compute the set described by the formula below.
\[ (\{f\} \cap \{d, a\}) \cup (\{d, a\} \cup \{f\}) \]
\[ \{d, f, a\} \]
Compute the set described by the formula below.
\[ \{c\} \cup (\{c\} - (\{c\} \cup \{e\})) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ \{\{e, c\}, \{\{e, c\}, \{b\}\}\} \cup (\{\{e, c\}, \{\{e, c\}, \{b\}\}\} \cup (\{e\} \cap \{c\})) \]
\[ \{\{e, c\}, \{\{e, c\}, \{b\}\}\} \]
Compute the set described by the formula below.
\[ (\{a\} \cup (\{a\} - \{e, a\})) \cup (\{e, a\} \cup \{a\}) \]
\[ \{e, a\} \]
Compute the set described by the formula below.
\[ (\{e\} \cup \{c\}) - (\{e\} - \{d\}) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ \{d, b\} \cap (\{d, b\} \cup (\{d, b\} \cup \{d, a\})) \]
\[ \{d, b\} \]
Compute the set described by the formula below.
\[ (\{b\} \cap \{e, f, b\}) \cup (\{e, f, b\} - \{b\}) \]
\[ \{e, f, b\} \]
Compute the set described by the formula below.
\[ (\{\{d, b\}, \{\{d, b\}, \{c\}\}\} \cap \{b\}) \cup (\{\{d, b\}, \{\{d, b\}, \{c\}\}\} - \{b\}) \]
\[ \{\{d, b\}, \{\{d, b\}, \{c\}\}\} \]
Compute the set described by the formula below.
\[ \{d\} \cup (\{d\} \cup (\{a\} - \{f, a, e\})) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ (\{d\} \cap (\{d\} \cap \{a\})) \cup (\emptyset \cup \{d\}) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ \{b\} \cap \{d, b\} \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ \{d\} - \{e\} \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ (\{a\} \cup (\{b\} \cap \{\{b\}, \{\{b\}, \{d\}\}\})) \cup (\{b\} \cap \{a\}) \]
\[ \{a\} \]
Compute the set described by the formula below.
\[ (\{d, f, b\} - \{d, a\}) \cup (\{d, f, b\} - \{d, a\}) \]
\[ \{f, b\} \]