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

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    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 ∅ = ∅.
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  2. #2
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    Quote Originally Posted by Grillakis View Post
    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.
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    Quote Originally Posted by ThePerfectHacker View Post
    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.
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