I'm trying to prove A ∩ B ∩ C ⊆ A ∩ B but am stuck after this:

Let x ∈ A ∩ B ∩ C

1. Therefore, x ∈ A and x ∈ B and x ∈ C

Question

I'm trying to prove A ∩ B ∩ C ⊆ A ∩ B but am stuck after this:

Let x ∈ A ∩ B ∩ C

1. Therefore, x ∈ A and x ∈ B and x ∈ C

jamesj · Answer

..hence it is true that x ∈ A and x ∈ B.  Therefore, x ∈ A ∩ B

anonymous · Answer

Thanks JamesJ, that's along the lines of what I thinking, but it seemed too...simple an explanation at the time. I need to practice this type of problem more.

jamesj · Answer

Keep at it!

jamesj · Answer

The basic logical principle here is this.  If X and Y are statements, then

X and Y ==> X

In other words, if you know two things are true, then each of their components is also true.