Discrete Mathematics and Its Applications |
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a₁ a₂ algorithm assigned Assume begin binary bit strings Boolean called circuit color combinations common complete condition connected Construct contains correct counting defined definition denoted described determine digits directed divides divisible edges elements equal equivalence EXAMPLE Exercise expansion expression false Figure final Find finite finite-state formula four function Give given grammar graph Hence illustrated initial input instance least length less letters loop machine mathematical induction matrix multiple namely needed Note obtained operations output pairs path permutation positive integer possible prime principle probability problem procedure proof proposition prove real numbers recurrence relation represent result root rule sequence Show shown in Figure Solution solve statement step string subset Suppose symmetric Table theorem transitive tree true variables vertex vertices