State whether each of the following relations is a partial ordering, and explain
ID: 3786711 • Letter: S
Question
State whether each of the following relations is a partial ordering, and explain why or why not.a) "isFatherOf" on the set of people
b) "isAncestorOf" on the set of people
c) "isOlderThan" on the set of people
d) "isSisterOf" on the set of people
e) {<a,b>, <a,a>, <b,a>} on the set {a, b}
f) {<2,1>, <1,3>, <2,3>} on the set {1, 2, 3}
Data Structures and Algorithm Analysis in C++ by Clifford Shaffer State whether each of the following relations is a partial ordering, and explain why or why not.
a) "isFatherOf" on the set of people
b) "isAncestorOf" on the set of people
c) "isOlderThan" on the set of people
d) "isSisterOf" on the set of people
e) {<a,b>, <a,a>, <b,a>} on the set {a, b}
f) {<2,1>, <1,3>, <2,3>} on the set {1, 2, 3}
Data Structures and Algorithm Analysis in C++ by Clifford Shaffer
a) "isFatherOf" on the set of people
b) "isAncestorOf" on the set of people
c) "isOlderThan" on the set of people
d) "isSisterOf" on the set of people
e) {<a,b>, <a,a>, <b,a>} on the set {a, b}
f) {<2,1>, <1,3>, <2,3>} on the set {1, 2, 3}
Data Structures and Algorithm Analysis in C++ by Clifford Shaffer
Explanation / Answer
a) FALSE - IsFatherOf on the set of male humans is not a partial ordering because it is not
transitive. If A isfather of B and B is father of C then it is not true that A is father
of C.
b) TRUE - IsAncestorOf on set of all humans is a partial order bcoz If A isAncestor of B and B is Acestor of C then it is true that A is Ancestor of C.
c)TRUE - IsOlderThan on set of all humans is a partial order bcoz If A IsOlder Than B and B is IsOlder Than C then it is true that A IsOlder Than C.
d)FALSE - isSisterOf on the set of all humans is not a partial ordering because it is not
transitive. If A isSister of B but it is not true that B isSister of C [it can be brother also]
e)FALSE - for any two element a,b if (a,b) is in the relation but (a,a) is not in the relation .It is not connected
f)TRUE - That is, for any three elements 1,2, and 3, if (1, 2) is in the relation and (2,3) is in the relation, then is (1, 3) also in the relation
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