Thread: 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.

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 it means that 1,3, and 5 are elements of B. if B has elements, then it is not empty.

Just by definition we know that
.
The how can B be empty??