tut08.pdf - Mat1101 Tutorial Week 8 Relationships and...

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Mat1101 Tutorial Week 8Relationships and FunctionsGrossman Chapter 5 and 61. Complete any outstanding tutorial questions from Week 7. (Catch up due to the publicholidays).2. Consider the relation β€œis greater than or equal to” on the set𝐴 = {1, 2, 3, 5}. Writedown the matrix representation for this relation. What is the set𝑹defined by thisrelation.3. Consider the relation𝑹defined on the setβ„€of integers as:π‘₯𝑹𝑦ifπ‘₯ βˆ’ 𝑦is divisible by3.(a) Starting with a subset of the integers:𝑍1= {βˆ’3, βˆ’2, βˆ’1, 0, 1, 2, 3},illustrate the subset defined by this relation.(b)ExtensionShow that𝑹is an equivalence relation and describe its equivalenceclasses.4. Grossman chapter 5 exercises p. 93–6 nos. 1–10, 15–205. Let𝑓 (π‘₯) =1π‘₯βˆ’2and𝑔(π‘₯) =√π‘₯ + 4be functions defined such that𝑓 ∢ ℝ β†’ ℝ. Find(a) The domain and range of𝑓and𝑔.(b) Evaluate
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Term
Fall
Professor
NoProfessor
Tags
Binary relation, Inverse function, Injective function

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