QUESTION 13 are both binary relations overs which are also functions, and define

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QUESTION 13 are both binary relations overs which are also functions, and define relations Functions are relations, and relations are sets, so we can do set operations on functions. Suppose R and t, = RU Q and V = RnQ . Then: suppose R?Q Neither U nar V is a function witn domains Only is a function with domain S Only is a function with domain s and v are both functions with domain s QUESTION 14 The relation { (a,0), (c, 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 functionf where) is the last name of the QUT student with student number x, the domnain off is: The set of last names for all students at QUT The set of strings of the form nxxxxxxX where the X's are digits. The set of student numbers for all stucents at QUT The set of strings of letters. QUESTION 16 Given the function f(x) =x2 defined on Z , the range off is: Z {0} 2

Explanation / Answer

13. If both R and Q are binary relations, the ( R Union Q) is not a function because it has multiple images for some of the elements. (R intersection Q) is also not a function because some elements might not have any image.

14. It is a function because each element has only one image. It doesn't have an inverse function because 3 will have two preimages. So, it's a function without inverse.

15.The domain of the function f(x) is x. Here x is the set of student numbers for all the students of QUT.

16.Given f(x)=x^2 for x taking both positive and negative integers. But f(x) will have all postive integers. So, range of f(x) is x=z^2 where z€Z.

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