Q: Let A be a set. Show that ∅ x A = A x ∅ = ∅.
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Originally Posted by Grillakis Q: Let A be a set. Show that ∅ x A = A x ∅ = ∅. Remember that $\displaystyle A\times B = \{ (x,y) | x\in A\text{ and }b\in B\}$. Therefore, $\displaystyle \emptyset \times A = \{(x,y) | x\in \emptyset \text{ and }b\in A \} = \emptyset$.
Originally Posted by ThePerfectHacker Remember that $\displaystyle A\times B = \{ (x,y) | x\in A\text{ and }b\in B\}$. Therefore, $\displaystyle \emptyset \times A = \{(x,y) | x\in \emptyset \text{ and }b\in A \} = \emptyset$. I see. Thanks. I'll remember that from now on. I think I forgot about that.
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