Math Problem Statement
Given that Set P = {1, 6, 8, 22, 42}, Q = {52, a, b, c, d, e, f} and R = {1, 18, 42, 16, c, g, d, h}, determine Q ∪ (P - R).
Solution
To solve this problem, we need to calculate given the following sets:
Step 1: Calculate
The operation represents the elements in that are not in .
- Elements of :
- Elements of :
Comparing each element in with :
- is in , so it is excluded.
- is not in , so it is included.
- is not in , so it is included.
- is not in , so it is included.
- is in , so it is excluded.
Thus, .
Step 2: Calculate
Now, we find the union of and , denoted by .
- Elements of :
- Elements of :
Taking the union of these two sets gives:
Final Answer:
Would you like further clarification on any step?
Here are five related questions that may deepen your understanding:
- How do we determine the elements in when both sets contain different types of elements (numbers and letters)?
- What is the meaning of the union operation in set theory?
- How would the result change if or were different?
- What would happen if we calculated instead of ?
- Can we determine with the given sets, and what would it represent?
Tip: Always double-check which elements are being removed in set difference operations, as it can easily lead to mistakes in complex sets.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Union
Set Difference
Formulas
A - B = {x | x ∈ A and x ∉ B}
A ∪ B = {x | x ∈ A or x ∈ B}
Theorems
Union of Sets
Set Difference
Suitable Grade Level
Grades 9-12