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Let $\text{R}_1, \text{R}_2, \ldots,\text{ }R_n$ be a decomposition of schema $\text{U}$. Let $u(\text{U})$ be a relation, and let $r_i=\Pi_{\text{R}_i}(u)$

Which of the following is true?

  1. $u \subseteq r_1 \bowtie r_2 \bowtie r_3 \bowtie r_4 \bowtie \ldots r_n$
  2. $u \supseteq r_1 \bowtie r_2 \bowtie r_3 \bowtie r_4 \bowtie \ldots r_n$
  3. $u=r_1 \bowtie r_2 \bowtie r_3 \bowtie r_4 \bowtie . . r_n$
  4. None of the above
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Option A – True for ALL decompositions.

Option C – True for Lossless decompositions.

Option B – Never true if proper superset was given.
Answer:

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