A belongs to b, b subset c, a not a subset of c

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SUMMARY

The discussion centers on the logical relationships between sets A, B, and C, specifically the conditions a∈b, b⊆c, and a not ⊆ c. Participants explore the implications of these relationships, concluding that if A, B, and C are empty sets, it contradicts the condition that a can be an element of B. The confusion arises from the definitions of element (∈) and subset (⊆), leading to a need for clarity on these concepts. A specific example provided is b = {1, 2, 3}, c = {1, 2, 3, 4}, and a = 1, which illustrates the relationships more clearly.

PREREQUISITES
  • Understanding of set theory, specifically the concepts of element (∈) and subset (⊆).
  • Familiarity with logical reasoning in mathematical contexts.
  • Basic knowledge of empty sets and their properties.
  • Ability to analyze and construct set relationships.
NEXT STEPS
  • Study the definitions and properties of elements and subsets in set theory.
  • Explore examples of set relationships to reinforce understanding of a∈b and b⊆c.
  • Learn about the implications of empty sets in set theory.
  • Practice solving problems involving set relationships and logical reasoning.
USEFUL FOR

Students of mathematics, particularly those studying set theory, educators teaching these concepts, and anyone seeking to improve their logical reasoning skills in mathematical contexts.

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Homework Statement


a∈b, b⊆c, a not ⊆ c
(in other words, the last subset symbol should have a line from top to bottom)

Homework Equations




none

The Attempt at a Solution



ive tried a million things, I can't find anything that doesn't break one of the conditions

the most recent attempt is that
A, B and C are all empty sets, but that would imply that a can be an element of B. my logic is that a doesn't contain all the elements of c, because there are no elements of c

every other thing I've tried has c containing all the elements of B, but since B contains all the elements of A, i run into a logical problem.

I tried for a long time on this one, and I really need help
 
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This might be an exercise in understanding what ∈ and ⊆ mean, but I'm not sure if you copied the problem correctly. Are you sure that's what it reads?
 
Consider b= {1, 2, 3}, c= {1, 2, 3, 4}, a= 1.
 

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