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The Venn diagram shows three sets P, Q and R. Use set notation to describe the shaded part.
Mathematics
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Step-by-step solution
4 stepsIdentify the individual shaded regions.
The shaded region consists of two distinct parts:
- The part where sets P and Q overlap, but set R does not.
- The part where sets P and R overlap, but set Q does not.
Express each region using set notation.
- The region where P and Q overlap is . If R does not overlap, we exclude R, which is . So this part is .
- The region where P and R overlap is . If Q does not overlap, we exclude Q, which is . So this part is .
Combine the regions using the union operator.
Since the shaded area includes both of these parts, we use the union () operator:
Simplify the expression (optional, but often preferred for conciseness).
We can factor out P from the expression:
The expression represents the symmetric difference between sets Q and R, often denoted as .
Therefore, the shaded region can also be described as:The final answer is or .
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