Consider the following two relational schemas:
- MovieExec(name, address, cert, netWorth)
- Studio(name, address, presC)
Suppose we wish to require that one must have a net worth of at least 10000$ Rupees to be president of a movie studio. The join operation if required can be performed on the attribute cert of MovieExec and PresC of Studio on equality condition. This join operation combines pairs of tuples consisting of a studio and an executive, such that the executive is the president of the studio. Which of the following expressions is/are best represent this constraint?
1
\({{\rm{\sigma }}_{{\rm{networth\;}} > {\rm{\;}}10000}}\left( {{\rm{MovieExec}}{{\rm{\;}⨝}_{{\rm{cert\;}} = {\rm{\;presC}}}}{\rm{studio}}} \right){\rm{\;}} \ne {\rm{\;}}\phi \)
2
\({{\rm{\sigma }}_{{\rm{networth\;}} < {\rm{\;}}10000}}\left( {{\rm{MovieExec}}{{\rm{\;}}⨝_{{\rm{cert\;}} = {\rm{\;presC}}}}{\rm{studio}}} \right){\rm{\;}} = {\rm{\;}}\phi \)
3
\({{\rm{\pi }}_{{\rm{presC}}}}\left( {{\rm{studio}}} \right){\rm{\;}} \subseteq {\rm{\;}}{{\rm{\pi }}_{{\rm{cert}}}}({{\rm{\sigma }}_{{\rm{networth\;}} > = {\rm{\;}}10000}}\left( {{\rm{MovieExec}}} \right))\)
4
\({{\rm{\pi }}_{{\rm{presC}}}}\left( {{\rm{studio}}} \right){\rm{\;}} \subseteq {\rm{\;}}{{\rm{\pi }}_{{\rm{cert}}}}({{\rm{\sigma }}_{{\rm{networth\;}} < = {\rm{\;}}10000}}\left( {{\rm{MovieExec}}} \right)){\rm{\;}}\)