How to determine the following sets (ex a ∪ {∅})

Question

Help! I don't know how to determine the following sets

The question was: Let A={∅,{∅},{{∅}}. Determine the following sets

• a∪{∅}
• a∩{∅}
• a∩{{∅},{∅,{∅}}}
• a∪{{∅},{∅,{∅}}}

Answer 1

a∪{∅} = a if ∅ in a.
Otherwise it is a with the additional element ∅.

a∩{∅} = {∅} if ∅ in a. Otherwise it is empty set.