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I am wondering what would be the result of the following operation:

Let $A$ be a relation with $n$ ($n > 0$) attributes and $t$ ($t > 0$) tuples. Let $TableDum$ be a relation with $0$ attributes and $0$ tuples. Let $TableDee$ be a relation with $0$ attributes and $1$ tuples.

What would the result of the following be? ($\times$ being the cross product)

$R_1 = A \times TableDum\\ R_2 = A \times TableDee$

Would $R_1$ be a relation with $n$ attributes or $0$ attributes? Would $R_1$ be a relation with $0$ tuples? Would $R_2$ be a relation with $n$ attributes or $0$ attributes? Would $R_2$ be a relation with $0$ tuples?

Thank you very much in advance.

M. Vinay
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Ludovic
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  • What are your own ideas on this? – M. Vinay Jun 17 '14 at 14:26
  • After some research, TableDum is the relational equivalent of true, and TableDee is the relational equivalent of false. R1 would then be equal to A without tuples. R2 would be equal to A. – Ludovic Jun 22 '14 at 11:48

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$$ A = R_1 \times TableDum = A_(empty)\\ A = R_2 \times TableDee = A $$

Ludovic
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