MHB Relation Algebra - Relational Calculus

AI Thread Summary
The discussion focuses on converting expressions from relational algebra to relational calculus. Several expressions were provided, and equivalent relational calculus representations were shared. There was a debate about the correct syntax, particularly regarding the use of tuples versus shorthand notation. Participants agreed that while shorthand might be acceptable in context, using tuples is the proper syntax for sets. The conversation concluded with confirmation that the initial expressions were generally correct.
mathmari
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Hey! :giggle:

Give for the following expressions of relation algebra the equivalent expression in relational calculus.
1. $\sigma_{B=A}(R(A,B,C))$
2. $\pi_{B,C}(R(A,B,C))$
3. $R(A,B,C)\cup S(A,B,C)$
4. $R(A,B,C)\cap S(A,B,C)$
5. $R(A,B,C)\setminus S(A,B,C)$
6. $R(A,B,C)\times S(D,C,E)$
7. $R(A,B,C)\Join S(B,C,E)$
8. $R(A,B) \div S(B)$I have done the following :

1. $\{x_1, x_2, x_3\mid R(x_1, x_2, x_3)\land (x_2=x_1)\}$
2. $\{y_1, y_2\mid \exists x_1\exists x_2\exists x_3 \left (R(x_1,x_2,x_3)\land y_1=x_2\land y_2=x_3\right )\}$
3. $\{x_1, x_2, x_3\mid R(x_1, x_2, x_3)\lor S(x_1, x_2, x_3)\}$
4. $\{x_1, x_2, x_3\mid R(x_1, x_2, x_3)\land S(x_1, x_2, x_3)\}$
5. $\{x_1, x_2, x_3\mid R(x_1, x_2, x_3)\land \neg S(x_1, x_2, x_3)\}$
6. $\{x_1, x_2, x_3, x_4, x_5, x_6\mid R(x_1,x_2,x_3) \land S(x_4,x_5,x_6)\}$
7. $\{ x_1, x_2, x_3, x_4 \mid R(x_1,x_2,x_3) \land S(x_2,x_3,x_4)\}$
8. $\{x_1 \mid R(x_1,x_2)\land S(x_2)\}$Is everything correct and complete? :unsure:
 
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Hey mathmari!

Shouldn't it be for instance $\{(x_1, x_2, x_3)\mid R(x_1, x_2, x_3)\land (x_2=x_1)\}$? 🤔

Otherwise I think everything is correct. (Sun)
 
Klaas van Aarsen said:
Shouldn't it be for instance $\{(x_1, x_2, x_3)\mid R(x_1, x_2, x_3)\land (x_2=x_1)\}$? 🤔

Otherwise I think everything is correct. (Sun)

Ah you mean that we should write them as tuples? :unsure:
 
mathmari said:
Ah you mean that we should write them as tuples? :unsure:
Yes. As far as I know, we have to, or it won't be correct syntax for sets.
Then again, it is clear what it means, so there is a chance that in the particular context it is considered to be an acceptable short hand abbreviation... 🤔
 
Klaas van Aarsen said:
Yes. As far as I know, we have to, or it won't be correct syntax for sets.
Then again, it is clear what it means, so there is a chance that in the particular context it is considered to be an acceptable short hand abbreviation... 🤔

Ah ok! I wrote the above in that way because I saw the below part in the notes :

1636395916131.png
 
mathmari said:
Ah ok! I wrote the above in that way because I saw the below part in the notes :

View attachment 11436
Ok. Then I guess it is just fine. (Sun)
 
Klaas van Aarsen said:
Ok. Then I guess it is just fine. (Sun)

Great! Thank you! (Sun)
 

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