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QUESTION 10 The equality relationon any set S is: A total ordering and a function with an inverse. An equivalence relation and also function with an inverse. A function with an inverse, and an equivalence relation with as single equivalence class equal to S An equivalence relation and also a total ordering QUESTION 11 A binary operation on a set S, takes any two elements a,b E S and produces another element c e S. Examples of binary operations include addition and multiplication on the set N. A binary operation is therefore: A partial ordering on S. A function with domain S and range S A binary relation over S A function with domain S x S and co-domain S QUESTION 12 Relations are just sets, so we can use set operations on them. Suppose that R and Q are both reflexive binary relations over S and define relations U = R U Q and V = R n . Then: Only U is a reflexive relation. U and V are both reflexive relations Only V is a reflexive relation. We don't have enough information to decide whether U or V is reflexive. QUESTION 13 Functions are relations, and relations are sets, so we can do set operations on functions. Suppose R and Q are both binary relations over S which are also functions. Suppose R and define relations U RuQand VRn. Then: Only U is a function with domain S. Only V is a function with domain S. Neither U nor V is a function with domain S U and V are both functions with domain S QUESTION 14 The relation {(a,0). (с.3).(b. 3), (d. 2)) O A function without an inverse. is: A function with an inverse. Not a function. Not a function, but has an inverse. QUESTION 15 Given the function f where f(r) is the last name of the QUT student with student numberx, the domain of f is: The set of strings of letters. The set of strings of the form nXXXXXXX, where the X's are digits. The set of student numbers for all students at QuT The set of last names for all students at QUT QUESTION 16 Given the function/(x) = x2 defined on Z, the range off is QUESTION 17 A recursive definition of some mathematical object: O Has at least one base case (defining the function for 0) and at least one case defined in terms of the the definition of the object itself. O Has at least one base case and at least one case defined in terms of the the definition of the object itself Cannot refer to the definition itself to avoid circularity O Has at least one case defined in terms of the the definition of the object itself QUESTION 18 Define the function f on R by f(x) = x :x>0 Then f is: Defined recursively, with two base cases. Not defined recursively, and f has no inverse Defined recursively, with one base case Not defined recursively andf has an inverse ︶ QUESTION 19 Define the function f on N by :x=0 0 f(x)1 Thenf is: Defined recursively, with one base case Not defined recursively Not defined recursively, and f has no inverse. etinedrecrsivey QUESTION 20 Lexicographic ordering on bit strings: bs afunction from b s nly spani drin to O Is a total ordering. Is not a partial ordering since it is not transitive

Answer 1

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