Relation Algebra - Relational Calculus

[mathmari]

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:

 

[I like Serena]

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)

 

[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)

Ah you mean that we should write them as tuples? :unsure:

 

[I like Serena]

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...

 

[mathmari]

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 :

 

[I like Serena]

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)

 

[mathmari]

Ok. Then I guess it is just fine. (Sun)

Great! Thank you! (Sun)