[See Steps] Let f:A→ B be a function. Show that the corresponding direct image function preserves all unions. Show that the corresponding inverse image
Question: Let \(f:A\to B\) be a function.
- Show that the corresponding direct image function preserves all unions.
- Show that the corresponding inverse image function preserves all unions, intersections, and set complements.
- Prove or disprove the following statement: the inverse image function
is inverse to the direct image function
\[\overset{\to }{\mathop{f}}\,:{{2}^{A}}\to {{2}^{B}}\]
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