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

[BloodyFrozen]

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...

 

[Mark44]

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.

 

[BloodyFrozen]

Took me a while to get what you are asking. It's the first.

Ok, thanks

 

[HallsofIvy]

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!