Let $R$ and $S$ be relational schemes such that $R=\{a,b,c\}$ and $S=\{c\}.$ Now consider the following queries on the database:
Select R.a,R.b From R,S Where R.c = S.c
Which of the above queries are equivalent?
1st one is R divide S
refer: http://users.abo.fi/soini/divisionEnglish.pdf page number 3
@Arjun Thank you sir for all the links provided it is very useful in understanding the concepts. Have you put up any blog which contains standard resources and links for all concepts/subjects?
So, $1$ and $2$ are equivalent. $$\overset{r}{\begin{array}{|c|c|c|} \hline \textbf{a} & \textbf {b} & \textbf {c} \\\hline \text{Arj }& \text{TY} & 12 \\\hline \text{Arj }& \text{TY} & 14 \\\hline \text{Cell }& \text{TR} & 13\\\hline \text{Tom }& \text{TW} & 12\\\hline \text{Ben }& \text{TE} & 14\\\hline \end{array}} \qquad \overset{s}{\begin{array}{|c|c|c|} \hline \textbf {c} \\\hline 12 \\\hline 14\\\hline \end{array}}$$
http://pages.cs.wisc.edu/~dbbook/openAccess/firstEdition/slides/pdfslides/mod3l1.pdf
Correct Answer: $A$
This question is just using different interpretations of “division” operator which is well explained in most DBMS textbooks (like Connolly for example). This link also has a good explanation: https://stackoverflow.com/questions/34978533/how-to-understand-u-r%C3%B7s-the-division-operator-in-relational-algebra
Everything about division operation explained by @Deepak Poonia Sir : Division Operation in Relational Algebra | BEST Detailed Complete Explanation | DBMS | Deepak Poonia - YouTube