Relational Algebra

Question

Two relations are R(A,B) and S(B,C) values all are integer

1.$\pi _{A,C}\left ( R\bowtie \sigma _{B=1}S \right )$

2.$\pi _{A}\left ( \sigma _{B=1}R \right )\times \pi _{C}\left ( \sigma _{B=1}S \right )$

3.$\pi _{A,C}\left ( \pi _{A}R\times \sigma _{B=1}S \right )$

Which of these three are equivalent?

What is easiest way to avoid error in such question

Comments

@ Rupendra Choudhary

yes , but every time random input doesnot give right output. 

Here where u put more attention in question?

In B=1 part right?

I mean how do u think after seeing this question, that it could give a right result?

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you raised nice point srestha. You have to be smart enough to guess the right input and believe me it's not much difficult.

By carefully observing the question and given options , we can guess the right input.

someone can come and take both relations NULL and then say all are equal which is supposed to be stupid enough.

with that skill you can solve many questions without even following any procedure and that's the advantage of objective type paper. THe given question is simple one which is asking the natural join of those elements of R,S for which B=1.

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As mentioned in comments you can take the example and solve this kind of problems. But be careful with what you choose, in general, try to include null, duplicates values in them.

Alternatively, you can try to find what the query does, but this can be time-consuming especially if you are new to these concepts. So with practice, these questions can be easily solved within 3 minutes. (time we have in GATE exam approximately)