Let me carefully examine the Venn diagrams and match each colored region to its correct set notation.
There are six Venn diagrams, each with colored regions, and below them are six set notation options:
- PUQ (which likely means P ∪ Q)
- $\overline{A \cap B}$
- A − B
- A ∩ B
- $\overline{A \cup B}$
- B − A
I need to identify what each colored region represents.
Let me go diagram by diagram:
1. First diagram (top-left): Two overlapping circles A and B inside universal set U; the
intersection (overlap) is colored yellow.
→ This is A ∩ B
2. Second diagram (top-middle): Circles P and Q; the
entire area covered by either P or Q (both circles, including overlap) is yellow.
→ This is P ∪ Q
3. Third diagram (top-right): Circles A and B inside U; the
background (outside both A and B) is yellow.
→ This is $\overline{A \cup B}$ (complement of union)
4. Fourth diagram (middle-left): A and B inside U; the part of A that does
not overlap with B is yellow (left crescent).
→ This is A − B
5. Fifth diagram (middle-center): A and B inside U; the part of B that does
not overlap with A is yellow (right crescent).
→ This is B − A
6. Sixth diagram (middle-right): A and B inside U; the
entire area except the intersection is yellow — i.e., everything in A or B but not in both.
→ That’s the complement of A ∩ B: $\overline{A \cap B}$
Now let’s match them to the boxes below (there are 6 blank boxes under the diagrams, and 6 options listed). The task says “Drag the set-notation...”, so we assign each notation to the correct diagram.
So the correct matches are:
- Diagram 1 (intersection colored) → A ∩ B
- Diagram 2 (union colored) → PUQ (i.e., P ∪ Q)
- Diagram 3 (outside both colored) → $\overline{A \cup B}$
- Diagram 4 (A only colored) → A − B
- Diagram 5 (B only colored) → B − A
- Diagram 6 (everything except intersection colored) → $\overline{A \cap B}$
Since the question asks to solve the problem accurately and only provide the final answer (and ExplainAnswer = false), I will list the correct set notation for each of the six diagrams in order (left to right, top to bottom).
Final Answer:
A ∩ B, PUQ, $\overline{A \cup B}$, A − B, B − A, $\overline{A \cap B}$
Parent Tip: Review the logic above to help your child master the concept of set notation worksheet.