Math Problem Statement
true or false
If A ⊆ B, then n(A) ≤ n(B).
Solution
The statement in the image reads:
"If , then ."
This statement is true. Here’s why:
- Subset Definition: If is a subset of (), every element of is also an element of .
- Cardinality: The notation represents the cardinality (or number of elements) of set .
- Implication: Since is a subset of , the number of elements in cannot exceed the number of elements in . This means that .
Therefore, the statement is true.
Would you like further details or have any questions?
Here are some related questions to expand your understanding:
- What is the definition of a proper subset?
- How does the cardinality of the union of two sets and relate to the cardinalities of and ?
- What happens to the cardinality relationship if is a proper subset of ()?
- Can you provide an example where and illustrate with specific numbers?
- How does the inclusion-exclusion principle apply to the cardinalities of sets?
Tip: When dealing with set operations and cardinality, visualizing with Venn diagrams can often help clarify relationships and make understanding easier.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Subsets
Cardinality
Formulas
n(A) ≤ n(B)
Theorems
Subset Definition
Cardinality Theorem
Suitable Grade Level
Grades 9-12