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Discrete Mathematics with Graph Theory (3rd Edition) 39

# Discrete Mathematics with Graph Theory (3rd Edition) 39 -...

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Section 2.3 37 7. [BB] The argument assumes that for a E n there exists a b such that (a, b) En. This need not be the case: See Exercise 5(g). 8. (a) [BB] Reflexive: Every word has at least one letter in common with itself. Symmetric: If a and b have at least one letter in common, then so do b and a. Not antisymmetric: (cat, dot) and (dot, cat) are both in the relation but dot =F cat!! Not transitive: (cat, dot) and (dot, mouse) are both in the relation but (cat, mouse) is not. (b) Reflexive: Let a be a person. If a is not enrolled at Miskatonic University, then (a, a) E n. On the other hand, if a is enrolled at MU, then a is taking at least one course with himself, so again (a, a) En. Symmetric: If (a, b) E n, then either it is the case that neither a nor b is enrolled at MU (so neither is b or a, hence, (b, a) E n) or it is the case that a and b are both enrolled and are taking at least one course together (in which caseb and a are enrolled and taking a common course, so (b, a) En). In any case, if (a, b) En, then (b, a) En.
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