Shade $C \cup A'$ on the given Venn diagram showing sets A, B, C, and the universal set U.
Understand the Problem
The question asks us to shade the region represented by $C \cup A'$ (C union A complement) on a Venn diagram with three sets A, B, and C within a universal set U. To do this, we first need to identify A', which includes everything in U that is NOT in A. Then, we need to find the union of C and A', which includes everything in C as well as everything that is not in A. We will need to shade this combined region on the Venn diagram.
Answer
The region $C \cup A'$ includes everything outside of $A$ as well as set $C$.
Answer for screen readers
U-
A
B
C
Here's the description of the shaded region:
Everything outside of A is shaded. Everything inside of C is shaded.
Steps to Solve
- Identify A' (the complement of A)
$A'$ represents everything in the universal set $U$ that is not in $A$. This means we need to consider all regions outside the circle representing set $A$.
- Identify C
$C$ represents everything inside the circle representing set $C$.
- Find the union of C and A' ($C \cup A'$ )
$C \cup A'$ means we need to combine everything in $C$ with everything in $A'$. This means we shade everything that is either in $C$ or in $A'$ (or in both). We shade the entire circle of $C$, and we shade everything outside the circle of $A$.
- Shade the Venn diagram
Based on the previous steps, we shade the entire area outside of circle $A$, and the entire circle $C$.
U-
A
B
C
Here's the description of the shaded region:
Everything outside of A is shaded. Everything inside of C is shaded.
More Information
The union of two sets includes all elements that are in either of the sets. The complement of a set includes all elements in the universal set that are not in the set.
Tips
A common mistake is to confuse the union symbol $\cup$ with the intersection symbol $\cap$. The union includes everything in either set, while the intersection includes only the elements that are in both sets.
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