Set Theory Symbols: Is A ∩ C ⊆ B Equal?

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Homework Help Overview

The discussion revolves around the interpretation of set theory symbols, specifically the expression involving the intersection of sets and subset relations. Participants are examining whether the expression A ∩ C ⊆ B is equivalent to (A ∩ C) ⊆ B or A ∩ (C ⊆ B).

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants express their thoughts on the order of operations in set notation and question the validity of the second expression involving a subset statement. There is an exploration of the meaning behind the intersection and subset relationships.

Discussion Status

Some participants suggest that the first interpretation is correct, while others clarify the distinction between set expressions and logical statements. There is an ongoing examination of the definitions and implications of the symbols used.

Contextual Notes

Participants note potential confusion arising from the mixing of set expressions with logical statements, highlighting the importance of understanding the nature of each component in the expressions being discussed.

BloodyFrozen
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Homework Statement



Is A ∩ C ⊆ B equal (A ∩ C) ⊆ B or A ∩ (C ⊆ B)?

Homework Equations



N/A

The Attempt at a Solution



I think it's the first one due to it being in order, but I'm not sure...
 
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BloodyFrozen said:

Homework Statement



Is A ∩ C ⊆ B equal (A ∩ C) ⊆ B or A ∩ (C ⊆ B)?


Homework Equations



N/A

The Attempt at a Solution



I think it's the first one due to it being in order, but I'm not sure...
Took me a while to get what you are asking. It's the first.
 
Mark44 said:
Took me a while to get what you are asking. It's the first.


Ok, thanks
 
The first,
[tex](A\cap B)\subset C[/tex]
is the statement that the set, [itex]A\cap B[/itex] is a subset of C.

The second,
[tex]A\cap (B\subset C)[/tex]
doen't make sense. The left side, A, is a set while the right side is NOT. The right side, [itex]B\subset C[/itex], is a statement that B is a subset of C. You can't take the intersection of a set with a statement!
 

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