Since both
ExplainAnswer and
TeachTopic are false, we will skip those sections entirely.
We are only to provide the
Final Answer, which in this case means describing what each Venn diagram should look like when shaded — since the task is to “Shade the Venn Diagrams” for each expression.
But note: The user did not ask for explanations or teaching — just to solve the problem accurately. Since the output format requires us to write reasoning *before* the Final Answer, and we must follow the structure even if options are false (except omitting the false sections), we’ll proceed by working through each problem step-by-step internally, then present the final shading instructions as the answer.
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Let’s go one by one:
1) Shade A’ - B’
This means: elements that are in A’ but NOT in B’.
- A’ = everything outside A
- B’ = everything outside B
- So A’ - B’ = elements outside A but inside B → that’s the part of B that doesn’t overlap with A.
✔ Shade: Only the part of circle B that does NOT overlap with A.
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2) Shade (A ∩ B)’
This means: everything that is NOT in both A and B.
- A ∩ B = the overlapping region
- So (A ∩ B)’ = everything except the overlap
✔ Shade: Everything EXCEPT the middle overlapping part.
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3) Shade (B - A)’
First, B - A = parts of B that are NOT in A → that’s the right-only part of B.
Then (B - A)’ = everything EXCEPT that right-only part of B.
✔ Shade: Everything except the part of B that doesn’t overlap with A.
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4) Shade A’ ∪ B’
This is “not A OR not B”.
By De Morgan’s Law: A’ ∪ B’ = (A ∩ B)’
So same as #2.
✔ Shade: Everything EXCEPT the overlapping region.
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5) Shade A
Simple: shade all of circle A.
✔ Shade: Entire circle A (including the part that overlaps with B).
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6) Shade A ∩ B
Intersection: only the overlapping region.
✔ Shade: Only the middle part where A and B overlap.
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Final Answer:
1) Shade only the part of B that does not overlap with A.
2) Shade everything except the overlapping region of A and B.
3) Shade everything except the part of B that does not overlap with A.
4) Shade everything except the overlapping region of A and B.
5) Shade the entire circle A.
6) Shade only the overlapping region of A and B.
Parent Tip: Review the logic above to help your child master the concept of union and intersection worksheet.
