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Exercise 8.1
1 |
Which of the following combinations are possible in a non-empty domain? Where a combination is possible, think of an example. Where it is not, why isn't it? | |
| (i) |
reflexive, asymmetric and transitive |
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| (ii) |
irreflexive, symmetric and transitive |
|
| (iii) |
irreflexive, non-symmetric and transitive |
|
| (iv) |
irreflexive, asymmetric and transitive |
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| (v) |
non-reflexive, connected, symmetric and transitive |
|
| (vi) |
irreflexive, connected, symmetric and transitive |
|
| (vii) |
connected, non-symmetric and transitive |
|
2 |
Given a domain consisting of all the people living in Oxford today, classify the following relations as reflexive, irreflexive or non-reflexive; symmetric, asymmetric or non-symmetric; transitive, intransitive or non-transitive; connected or not connected: | |
| (i) |
x is a brother or sister of y |
|
| (ii) |
x is married to y |
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| (iii) |
x is y's wife |
|
| (iv) |
x is at least six inches taller than y |
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| (v) |
x is not at least six inches taller than y |
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| (vi) |
x is at least ten feet taller than y |
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| (vii) |
x is not at least ten feet taller than y |
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| (viii) |
x plays in the same team as y |
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3 |
Classify the relation x is not the same person as y as reflexive, irreflexive or non-reflexive; symmetric, asymmetric or non-symmetric; transitive, intransitive or non-transitive; connected or not connected in the following domains: |
|
| (i) |
the domain consisting of all philosophers |
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| (ii) |
the domain whose only member is Descartes |
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| (iii) |
the domain whose only members are Descartes and Mill. |
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