Chapter 9: Q10E (page 590)
What do you obtain when you apply the selection operator \({s_C}\), where\(C\)is the condition Room \( = {\rm{A}}100\)to the table 7?
The resultant answer is explained.
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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?
Show that if \({C_1}\) and \({C_2}\) are conditions that elements of the \(n\)-ary relation \(R\) may satisfy, then \({s_{{C_1} \wedge {C_2}}}(R) = {s_{{C_1}}}\left( {{s_{{C_2}}}(R)} \right)\).
Find the error in the "proof" of the following "theorem."
"Theorem": Let \(R\) be a relation on a set \(A\) that is symmetric and transitive. Then \(R\) is reflexive.
"Proof": Let \(a \in A\). Take an element \(b \in A\) such that \((a,b) \in R\). Because \(R\) is symmetric, we also have \((b,a) \in R\). Now using the transitive property, we can conclude that \((a,a) \in R\) because \((a,b) \in R\)and \((b,a) \in R\).
Show that the relationon a non-empty set is symmetric and transitive, but not reflexive.
To draw the Hasse diagram for divisibility on the set \(\{ 1,2,4,8,16,32,64\} \).
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