# Homework Help: Set theoretical products

1. Jul 29, 2016

### rmiller70015

1. The problem statement, all variables and given/known data
Let S be any set and T = ∅. What can you say about the set S×T?

2. Relevant equations

3. The attempt at a solution
The solution is that S×T=∅. I'm not quite sure why this is though. Is it because there isn't anything in T to give an ordered pair so S×T is empty?

2. Jul 29, 2016

### PeroK

Can you find anything in $S \times T$?

3. Jul 29, 2016

### Math_QED

Well, when we write out the definition of AxB, we have:

AxB = {(a,b) | a ∈ A and b ∈ B}

Now, apply this to your set, what do you notice?

4. Jul 29, 2016

### rmiller70015

There is no element t for the set T. And the set theoretical product does not make sense. Except for (∅,∅).

5. Jul 29, 2016

### PeroK

$\emptyset \notin \emptyset$

6. Jul 29, 2016

### Math_QED

Let SxT = {(s,t)|s ∈ S and t ∈ T}
Suppose that SxT ≠ ∅...

Try to find a contradiction, then follows that S x T = ∅

7. Jul 30, 2016

### rmiller70015

Ok thank you, that makes sense.