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Best answer
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The decomposition of $R=\left \{ R1,R2 \right \}$ is a lossless or non-additive if atleast one of the dependencies

  • $R1\cap R2\rightarrow R1$
  • $R1\cap R2\rightarrow R2$

belong to $F^{+}$ :- Closure of the set of functional dependencies .

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The Decomposition D is lossless then it should satisfy any of the below two:

  1. (R1 ∩ R2) → (R1-R2) or 
  2.  R1 ∩ R2) → (R2-R1)

consider the ex: R(ABCDEF) which is decomposed into R1(ABCD) and R2(CDEF) , then this Decomposition becomes lossless when any of the below 2 satisfies:

  1. CD → AB or
  1. CD → EF

Therefore, I can say option C is correct.

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