MAT102H5 Final: MAT102H5_Final_Unknown_Unknown
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MAT102H5 Full Course Notes
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Each question is worth 2 marks. : in the following venn diagrams, shade the region that corresponds to the given set. (a) (a b) c (b) You may use the symbols (cid:54)= and/or (cid:54) , if necessary. P q p (( q) p ) Let y f (c d) . Then y = f (x) for some x c d . This implies that x c and x d . We therefore conclude that y = f (x) is an element of both f (c) and f (d) , and hence in f (c) f (d). This proves that f (c d) f (c) f (d) . 3 (b) give an example of a function f , and sets c, d , for which f (c d) (cid:54)= f (c) f (d) . Take f (x) = x2 , and let c = [ 1, ) and d = ( , 1] .
