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What do you obtain when you apply the selection operator \({s_C}\), where \(C\) is the condition (Airline = Nadir) \( \vee \) (Destination = Denver), to the database in Table 8?

Short Answer

Expert verified

(Nadir, 122, 34, Detroit, 08:10), (Nadir, 199, 13, Detroit, 08:47), (Nadir, 322, 34, Detroit, 09:44), (Acme, 221, 22, Denver, 08:17), and (Acme, 222, 22, Denver, 09:10).

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01

Given data

Table 8 is given.

02

Concept of sets

The concept of set is a very basic one. It is simple; yet, it suffices as the basis on which all abstract notions in mathematics can be built.\(A\)set is determined by its elements. If\(A\)is a set, write\(x \in A\)to say that\(x\)is an element of\(A\).

03

Simplify the expression

The selection operator picks out all the tuples that match the criteria.

The 5-tuples in Table 8 that have Nadir as their airline are (Nadir, 122, 34, Detroit, 08: 10), (Nadir, 199, 13, Detroit, 08: 47), and (Nadir, 322, 34, Detroit, 09: 44).

The 5-tuples in Table 8 that have Denver as their destination are (Acme, 221, 22, Denver, 08: 17) and (Acme, 222, 22, Denver, 09: 10).

The union of these two lists:

(Nadir, 122, 34, Detroit, 08:10), (Nadir, 199, 13, Detroit, 08:47), (Nadir, 322, 34, Detroit, 09:44), (Acme, 221, 22, Denver, 08:17), and (Acme, 222, 22, Denver, 09:10).

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Most popular questions from this chapter

FindRยฏfor the given R.

Exercises 34โ€“37 deal with these relations on the set of real numbers:

\({R_1} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a > b} \right\},\)the โ€œgreater thanโ€ relation,

\({R_2} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a \ge b} \right\},\)the โ€œgreater than or equal toโ€ relation,

\({R_3} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a < b} \right\},\)the โ€œless thanโ€ relation,

\({R_4} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a \le b} \right\},\)the โ€œless than or equal toโ€ relation,

\({R_5} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a = b} \right\},\)the โ€œequal toโ€ relation,

\({R_6} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a \ne b} \right\},\)the โ€œunequal toโ€ relation.

35. Find

(a) \({R_2} \cup {R_4}\).

(b) \({R_3} \cup {R_6}\).

(c) \({R_3} \cap {R_6}\).

(d) \({R_4} \cap {R_6}\).

(e) \({R_3} - {R_6}\).

(f) \({R_6} - {R_3}\).

(g) \({R_2} \oplus {R_6}\).

(h) \({R_3} \oplus {R_5}\).

The 5-tuples in a 5-ary relation represent these attributes of all people in the United States: name, Social Security number, street address, city, state.

a) Determine a primary key for this relation.

b) Under what conditions would (name, street address) be a composite key?

c) Under what conditions would (name, street address, city) be a composite key?

Let \(R\) the relation \(\{ (1,2),(1,3),(2,3),(2,4),(3,1)\} \) and \(S\) be the relation \(\{ (2,1),(3,1),(3,2),(4,2)\} \). Find \(S \circ R\).

Show that if \(C\) is a condition that elements of the \(n\)-ary relation \(R\)and \(S\)may satisfy, then \({s_C}(R - S) = {s_C}(R) - {s_C}(S)\).

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