# Set Theory Question

• Oct 7th 2007, 01:51 PM
nicole0714
Set Theory Question
Hi,

Just when I think I have my head wrapped around this stuff, I run into a wall. Here is my problem:

If A∩B={1,3,5}, then B≠ { }

Can someone tell me if this is true or false? If it is false I also need an explanation.

My answer is False because { } is a subset of B which probably makes no sense.

Any help is appreciated.
• Oct 7th 2007, 01:56 PM
Jhevon
Quote:

Originally Posted by nicole0714
Hi,

Just when I think I have my head wrapped around this stuff, I run into a wall. Here is my problem:

If A∩B={1,3,5}, then B≠ { }

Can someone tell me if this is true or false? If it is false I also need an explanation.

My answer is False because { } is a subset of B which probably makes no sense.

Any help is appreciated.

of course it is true. if $\displaystyle A \cap B = \{ 1,3,5 \}$ it means that 1,3, and 5 are elements of B. if B has elements, then it is not empty.
• Oct 7th 2007, 01:57 PM
Plato
Just by definition we know that
$\displaystyle 3 \in A \cap B\quad \Rightarrow \quad 3 \in A \wedge 3 \in B$.
The how can B be empty??