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

AI Thread Summary
The discussion centers on the relationship between set theory symbols, specifically whether A ∩ C ⊆ B is equivalent to (A ∩ C) ⊆ B or A ∩ (C ⊆ B). The consensus is that the correct interpretation is (A ∩ C) ⊆ B, as it maintains the proper order of operations. The alternative, A ∩ (C ⊆ B), is deemed nonsensical because it attempts to intersect a set with a statement rather than another set. This highlights the importance of understanding set operations and their syntax in set theory. Overall, clarity in notation is crucial for accurate mathematical communication.
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,
(A\cap B)\subset C
is the statement that the set, A\cap B is a subset of C.

The second,
A\cap (B\subset C)
doen't make sense. The left side, A, is a set while the right side is NOT. The right side, B\subset C, 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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