Chapter 9: Q42E (page 616)
To determine collections of subsets are partitions of \(\{ - 3, - 2, - 1,0,1,2,3\} \).
The collection of subsets \(\{ \{ - 3,2,3\} ,\{ - 1,1\} \} \) is not a partition of set.
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Which projection mapping is used to delete the first, second, and fourth components of a 6-tuple?
Exercises 34–37 deal with these relations on the set of real numbers:
\({R_1} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a > b} \right\},\)the “greater than” relation,
\({R_2} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a \ge b} \right\},\)the “greater than or equal to” relation,
\({R_3} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a < b} \right\},\)the “less than” relation,
\({R_4} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a \le b} \right\},\)the “less than or equal to” relation,
\({R_5} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a = b} \right\},\)the “equal to” relation,
\({R_6} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a \ne b} \right\},\)the “unequal to” relation.
34. Find
(a) \({R_1} \cup {R_3}\).
(b) \({R_1} \cup {R_5}\).
(c) \({R_2} \cap {R_4}\).
(d) \({R_3} \cap {R_5}\).
(e) \({R_1} - {R_2}\).
(f) \({R_2} - {R_1}\).
(g) \({R_1} \oplus {R_3}\).
(h) \({R_2} \oplus {R_4}\).
Which 4-tuples are in the relation \(\{ (a,b,c,d)\mid a,b,c\), and \(d\) are positive integers with \(abcd = 6\} \) ?
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?
(a)To find the number of relations on the set \(\{ a,b,c,d\} \).
(b)To find the number of relations on the set \(\{ a,b,c,d\} \) contain the pair \((a,a)\).
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