Identify and shade the following regions on separate venn diagram
1 answer:
The attached figures represent the shaded areas of the given set operations
<h3>How to identify the shaded regions?</h3>To shade the given regions of the sets, we need to highlight the following set operations
- Intersection: This represents the elements that are common between two or more sets
- Union: This represents the totality of all elements in two or more sets (without repetition of elements)
- Complement: This represents the elements that are not present in the given set
Using the above definition of set operations and the Venn diagram, we have the following values:
- X U Y' = Y'
- X n Y' = ∅ i.e an empty set
- (X U Y)' = X' n Y'
- (X n Y)' = U i.e. the universal set
- X' U Y' = X' n Y'
- X' n Y' = X' U Y'
- (X' U Y)' = X
- (X U Y')' = Y
See attachment for the shaded areas of the above set operations
Read more about sets and Venn diagram at:
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Answer:
a) SPAZ is equilateral.
b) Diagonals SA and PZ are perpendicular to each other.
c) Diagonals SA and PZ bisect each other.
Step-by-step explanation:
At first we form the triangle with the help of a graphing tool and whose result is attached below. It seems to be a paralellogram.
a) If figure is equilateral, then SP = PA = AZ = ZS:
Therefore, SPAZ is equilateral.
b) We use the slope formula to determine the inclination of diagonals SA and PZ:
Since , diagonals SA and PZ are perpendicular to each other.
c) The diagonals bisect each other if and only if both have the same midpoint. Now we proceed to determine the midpoints of each diagonal:
Then, the diagonals SA and PZ bisect each other.
