relational algebra

Question

In the following relational algebra expressions, assume union and difference are multi set operators and the relations R(x),S(x) and T(x) are multi sets.

Q1:(R U S)-T

Q2:(R - T)U(S - T)

(A) Q1 and Q2 produce the same answer

(B) The answer to Q1 is always contained in the answer to Q2

(C) The answer to Q2 is always contained in the answer to Q1

(D) They produce complete different answers

what is the answer ,please explain or give example.

Answer 1

The answer is (C).

First we show that Q2 $\subseteq$ Q1. Lets consider some examples.

  R                                        S                                              T

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1  1                                   1  2                                       2   1

1  2                                   2  1                                       2   2

2  1                                   2  2                                       2   3

 

Q1: (1,1) (1,2) (1,2) (2,1)

Q2: (1,1) (1,2) (1,2)

Hence, proved.

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Now, we disprove that Q1 $\subseteq$ Q2 is ever possible.

Q1 is subtracting T only once while Q2 is subtracting T twice. So, possiblity of having tuples in Q1 more than Q2 is necessarily more than Q2.

Hence, Q1 $\subseteq$ Q2 is never possible.

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Hence, answer (C).

Comments

I think R$\cup$S will have not redundant tuple i.e.. (1,2) and (2,1) will appear once.So by subtracting T will produce same result as Q2.

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@indrajeet. Given that union is multiset operation.

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multiset operation means what??

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SQL operation 1) union all 2) intersect all 3) minus all

Answer 2

I draw Venn Diagram and got Q1 and Q2 both are Same.

Option is A.

Answer 3

crt option is A  Q1 and Q2 results the same