Exercises with set operations (Batch 1)
Compute the set described by the formula below.
\[ (\{f, b\} \cup (\{f, b\} - \{b, d\})) \cap (\{e\} \cup \{b, d\}) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ \{d\} - \{b, a\} \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ \{\{\{c, a\}, \{a\}\}, \{c, a\}\} - \{a\} \]
\[ \{\{\{c, a\}, \{a\}\}, \{c, a\}\} \]
Compute the set described by the formula below.
\[ (\{a\} \cap \{c\}) - (\{a\} \cap \{c\}) \]
\[ \emptyset \]
Compute the set described by the formula below.
\[ \{e, d\} - \{f\} \]
\[ \{e, d\} \]
Compute the set described by the formula below.
\[ (\{b, e\} \cup (\{b\} \cap \{f\})) - (\{b\} - \{f\}) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ \{\emptyset, \{\emptyset, \{f\}, \{b, e\}\}\} - (\{a\} \cap (\{\emptyset, \{\emptyset, \{f\}, \{b, e\}\}\} \cup \{e\})) \]
\[ \{\emptyset, \{\emptyset, \{f\}, \{b, e\}\}\} \]
Compute the set described by the formula below.
\[ \{b, e\} - (\{f\} \cup (\{b, e\} \cap \{f\})) \]
\[ \{b, e\} \]
Compute the set described by the formula below.
\[ (\{b\} \cup \{e\}) - (\{b\} \cup \{c\}) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ \{c\} \cap (\{c\} \cup (\{e\} \cap \{c\})) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ \{d, c\} \cap \{c\} \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ \emptyset \cup (\{b, e\} \cap \{b\}) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ (\{b\} \cap \{e\}) \cup (\{b\} \cup \{e\}) \]
\[ \{b, e\} \]
Compute the set described by the formula below.
\[ \{e\} \cap (\{e\} - (\{e, d\} - \{e\})) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ \{c\} \cup (\{c\} \cap \{a\}) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ (\{a\} \cup \{d\}) \cup (\{a\} \cap \{d\}) \]
\[ \{d, a\} \]
Compute the set described by the formula below.
\[ \{a\} \cap (\{d, a\} \cup (\{d, a\} \cap \{a\})) \]
\[ \{a\} \]
Compute the set described by the formula below.
\[ \{f\} - \{d\} \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ (\{a\} - \{e\}) - (\{a\} \cap \{f\}) \]
\[ \{a\} \]
Compute the set described by the formula below.
\[ (\{e\} - \{f\}) \cap (\{e\} - \{f\}) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ \{f, c\} - (\{f\} - (\{f\} - \{f, c\})) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ \{c, a\} \cup \{e\} \]
\[ \{c, e, a\} \]
Compute the set described by the formula below.
\[ (\{f\} \cup (\{f\} \cup \{b, c\})) \cap (\{f\} \cup \{b, c\}) \]
\[ \{f, b, c\} \]
Compute the set described by the formula below.
\[ (\{b\} \cap (\{b\} - \{c\})) \cap (\{b\} - \{c\}) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ \emptyset \cup \{e\} \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ (\{\{f\}, \{\{f\}, \{e\}, \{d\}\}\} - (\{c\} \cup \{\{f\}, \{\{f\}, \{e\}, \{d\}\}\})) \cup (\{\{f\}, \{\{f\}, \{e\}, \{d\}\}\} - \{c\}) \]
\[ \{\{\{f\}, \{e\}, \{d\}\}, \{f\}\} \]
Compute the set described by the formula below.
\[ (\{f, c\} \cup \{c\}) - (\{c\} \cup \{e, c\}) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ \{b\} \cap (\{b\} \cup (\{b\} - \{f\})) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ \{\{c\}, \{\{c\}, \{a\}\}\} - (\{d, a\} \cap (\{f\} \cap \{\{c\}, \{\{c\}, \{a\}\}\})) \]
\[ \{\{c\}, \{\{c\}, \{a\}\}\} \]
Compute the set described by the formula below.
\[ (\{a\} \cap \{f, e\}) - (\{b\} \cup \{f, c\}) \]
\[ \emptyset \]
Compute the set described by the formula below.
\[ (\{f, b\} \cap \{c\}) - (\{c\} \cap \{f, b\}) \]
\[ \emptyset \]
Compute the set described by the formula below.
\[ (\emptyset \cup \{b, d\}) \cup (\{b, d\} \cup \emptyset) \]
\[ \{b, d\} \]
Compute the set described by the formula below.
\[ \{f, e\} - (\{f\} \cap \{e\}) \]
\[ \{f, e\} \]
Compute the set described by the formula below.
\[ \{b\} \cup (\emptyset \cup \{f\}) \]
\[ \{f, b\} \]
Compute the set described by the formula below.
\[ \{d\} \cup (\{d\} - (\{d\} \cup \{a\})) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ (\{e\} - \{c\}) \cap (\{e\} - \{c\}) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ \{b, e\} \cup (\{b, e\} \cap (\{b, e\} \cup \{e\})) \]
\[ \{b, e\} \]
Compute the set described by the formula below.
\[ (\{f, c\} - (\{\{b, d\}, \{\{b, d\}\}\} \cap \{f, c\})) \cup (\{e\} \cap \{\{b, d\}, \{\{b, d\}\}\}) \]
\[ \{f, c\} \]
Compute the set described by the formula below.
\[ \{d\} - (\{\{a\}, \{\{a\}, \{d\}\}\} \cap (\{d\} - \{b\})) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ \{\{\emptyset, \{e, d\}\}, \{e, d\}\} \cap (\{\{\emptyset, \{e, d\}\}, \{e, d\}\} - (\{\{\emptyset, \{e, d\}\}, \{e, d\}\} - \{d\})) \]
\[ \emptyset \]
Compute the set described by the formula below.
\[ \{b\} \cup \{f\} \]
\[ \{f, b\} \]
Compute the set described by the formula below.
\[ \{a\} - (\{c\} - (\{c\} - \{a\})) \]
\[ \{a\} \]
Compute the set described by the formula below.
\[ (\{e\} \cup \{f\}) - (\{e\} \cup \{e\}) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ \{e, c\} - \{b\} \]
\[ \{e, c\} \]
Compute the set described by the formula below.
\[ \{c\} \cup (\{c\} - (\{c\} \cap \{c\})) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ (\{e\} - (\{b\} \cap \{e\})) - (\{e\} \cap \{b\}) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ \{\{\{e, c\}, \{b\}\}, \{b\}\} \cup (\{f, d\} - (\{\{\{e, c\}, \{b\}\}, \{b\}\} \cap \{f, d\})) \]
\[ \{\{\{e, c\}, \{b\}\}, \{b\}, d, f\} \]
Compute the set described by the formula below.
\[ (\{f\} - \{e\}) - (\{f\} \cap \{e\}) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ (\{f, d\} - \{f\}) - (\{f\} \cap \{f, d\}) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ \{d\} - (\{e\} - (\{b, c\} \cup \{d\})) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ \{d, a\} \cup (\{\{\{b\}, \{a\}\}, \{b\}\} - (\{\{\{b\}, \{a\}\}, \{b\}\} - \{d, a\})) \]
\[ \{d, a\} \]
Compute the set described by the formula below.
\[ \{e, c\} - (\{d\} \cap (\{e, c\} - \{f\})) \]
\[ \{e, c\} \]
Compute the set described by the formula below.
\[ \{b, a\} \cup (\{b, a\} - (\{b, a\} - \{c\})) \]
\[ \{b, a\} \]
Compute the set described by the formula below.
\[ \{b\} \cup (\{b\} \cap (\{b\} - \{e\})) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ (\{e\} \cup (\{e, c\} \cup \{a\})) \cup (\{a\} \cup \{e, a\}) \]
\[ \{a, c, e\} \]
Compute the set described by the formula below.
\[ \{b\} - (\emptyset \cup (\{f\} - \{b\})) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ (\{e\} \cap \{e, d\}) \cap (\{e, d\} \cap \{e\}) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ (\{d\} \cap \{a\}) \cup (\{a\} - \{d\}) \]
\[ \{a\} \]
Compute the set described by the formula below.
\[ (\{f, b\} \cap \{a\}) \cup (\{f\} - \{c\}) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ \{f, d\} \cap (\{f, d\} - (\{f, d\} - \{f\})) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ (\emptyset \cup \{e\}) \cup (\{d\} - \{e\}) \]
\[ \{e, d\} \]
Compute the set described by the formula below.
\[ (\{d, c\} - (\{e\} - \{d, c\})) \cup (\{e\} - \{b\}) \]
\[ \{e, d, c\} \]
Compute the set described by the formula below.
\[ \{c\} - (\emptyset - (\emptyset \cup \{c\})) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ (\{d, c\} \cap \{d, a\}) \cup (\{b, a\} - \{d, a\}) \]
\[ \{b, d\} \]
Compute the set described by the formula below.
\[ \{d, c\} - \{c\} \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ \emptyset \cup (\{e\} \cup (\{a, c\} \cup \{e\})) \]
\[ \{c, e, a\} \]
Compute the set described by the formula below.
\[ (\{b\} \cup (\{e\} \cup \{e\})) - (\{b\} - \{e\}) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ (\{d\} \cap \{a, c\}) \cup (\{f, b\} - \{a, c\}) \]
\[ \{f, b\} \]
Compute the set described by the formula below.
\[ \{a\} \cap (\{a\} - \{a\}) \]
\[ \emptyset \]
Compute the set described by the formula below.
\[ (\{a\} \cap \{f\}) \cup (\{f\} - \{a\}) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ (\{c\} \cup \emptyset) \cup (\{c\} - \emptyset) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ \{b\} \cup \{c\} \]
\[ \{b, c\} \]
Compute the set described by the formula below.
\[ \{d\} - \{e\} \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ \{e\} - \{\{\{e\}, \{a\}\}, \{e\}\} \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ (\{f\} \cup \{b\}) \cap (\{f\} \cap \{b\}) \]
\[ \emptyset \]
Compute the set described by the formula below.
\[ (\{a\} \cap \{c\}) \cup (\{c\} \cup \{a\}) \]
\[ \{a, c\} \]
Compute the set described by the formula below.
\[ \{e\} \cap (\{e, d\} \cup (\{e\} \cup \emptyset)) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ (\emptyset - \{a\}) \cup (\{a\} \cap \emptyset) \]
\[ \emptyset \]
Compute the set described by the formula below.
\[ \{b\} \cup (\{d, c\} - (\{d, c\} - \{b\})) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ \{d\} - (\{d\} - (\{d\} \cap \{d\})) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ \{f, a\} \cup (\{f, a\} - (\{f, a\} - \emptyset)) \]
\[ \{f, a\} \]
Compute the set described by the formula below.
\[ (\{d, c\} - \{c\}) \cup (\{c\} - \{a, c\}) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ \{f\} \cup (\{f\} \cup (\{f\} \cap \{f\})) \]
\[ \{f\} \]
Compute the set described by the formula below.
\[ \{b\} \cup \{e, a\} \]
\[ \{b, e, a\} \]
Compute the set described by the formula below.
\[ (\{e\} - (\{c\} - \{e\})) \cup (\{e\} \cap \{c\}) \]
\[ \{e\} \]
Compute the set described by the formula below.
\[ (\{b, d\} - \{a\}) \cup (\{e, a\} \cap \{a\}) \]
\[ \{b, d, a\} \]
Compute the set described by the formula below.
\[ (\{b\} \cap \{b, c\}) \cup (\{b, c\} - \{f, b\}) \]
\[ \{b, c\} \]
Compute the set described by the formula below.
\[ \{b\} \cup (\{b\} \cap (\{b\} \cap \{b, a\})) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ \{d\} - (\{e, a\} \cap (\{e, c\} \cup \{d\})) \]
\[ \{d\} \]
Compute the set described by the formula below.
\[ \{d\} - (\{d\} \cup (\{d\} \cup \emptyset)) \]
\[ \emptyset \]
Compute the set described by the formula below.
\[ \{b, a\} \cup (\{a, c\} \cap (\{f\} \cap \{b, a\})) \]
\[ \{b, a\} \]
Compute the set described by the formula below.
\[ \{e, c\} \cap (\{\{\{e, d\}, \{a\}\}, \{a\}\} \cup \{c\}) \]
\[ \{c\} \]
Compute the set described by the formula below.
\[ (\{b\} \cap (\{b\} \cup \{f\})) \cap (\{b\} \cup \{f\}) \]
\[ \{b\} \]
Compute the set described by the formula below.
\[ \emptyset \cup (\{a\} - (\{e\} - \{a\})) \]
\[ \{a\} \]
Compute the set described by the formula below.
\[ \{a\} - (\emptyset \cap (\emptyset \cap \{f, c\})) \]
\[ \{a\} \]
Compute the set described by the formula below.
\[ \{\{b\}, \{\{b\}, \{b, e\}\}\} \cup (\{\{b\}, \{\{b\}, \{b, e\}\}\} - (\{\{b\}, \{\{b\}, \{b, e\}\}\} \cup \{c\})) \]
\[ \{\{b\}, \{\{b\}, \{b, e\}\}\} \]
Compute the set described by the formula below.
\[ (\{b, d\} - (\{a\} - \{b, d\})) \cap (\{b, d\} \cup \{a\}) \]
\[ \{b, d\} \]
Compute the set described by the formula below.
\[ (\{f, a\} \cup \{d, c\}) \cup (\{f, a\} - \{d, c\}) \]
\[ \{a, c, f, d\} \]
Compute the set described by the formula below.
\[ \{b, c\} \cup (\{b\} - (\{b, a\} \cap \{b, c\})) \]
\[ \{b, c\} \]
Compute the set described by the formula below.
\[ (\{b\} - \{a\}) - (\{b\} \cap \{a\}) \]
\[ \{b\} \]