Math Problem Statement
Let U = {p, q, r, s, t}, D = {p, r, s, t}, E = {q, s}, F = {r, s}, and G = {s}. Determine whether the statement is true or false. F ⊂ D
Solution
The statement means that set is a subset of set . A set is a subset of another set if all elements of are also elements of .
Let's check this:
- Set
- Set
Now, look at the elements of :
- Element is in .
- Element is in .
Since all elements of are in , we can conclude that:
Therefore, the statement is true.
Would you like any further details or have any questions?
Here are 5 related questions to explore:
- What is the difference between a subset and a proper subset?
- Can a set be a subset of itself?
- What does mean, and how is it different from ?
- Is the empty set a subset of all sets?
- If , is ?
Tip: A set is always a subset of itself, but it is only a proper subset if it doesn't contain all elements of the other set.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Subsets
Formulas
Subset Definition: A is a subset of B if every element of A is also an element of B.
Theorems
Subset Theorem: A set A is a subset of a set B if every element of A is in B.
Suitable Grade Level
Grades 6-8