Math Help - How do I solve this?? Let A be a set. Show that ∅ x A = A x ∅ = ∅.

1. How do I solve this?? Let A be a set. Show that ∅ x A = A x ∅ = ∅.

Q: Let A be a set. Show that x A = A x ∅ = ∅.

2. Originally Posted by Grillakis
Q: Let A be a set. Show that x A = A x ∅ = ∅.
Remember that $A\times B = \{ (x,y) | x\in A\text{ and }b\in B\}$.
Therefore, $\emptyset \times A = \{(x,y) | x\in \emptyset \text{ and }b\in A \} = \emptyset$.

3. Originally Posted by ThePerfectHacker
Remember that $A\times B = \{ (x,y) | x\in A\text{ and }b\in B\}$.
Therefore, $\emptyset \times A = \{(x,y) | x\in \emptyset \text{ and }b\in A \} = \emptyset$.
I see. Thanks. I'll remember that from now on. I think I forgot about that.