Problem 13. Give an example of two subsets of R2 that are homotopy equivalent but not homeomorphic. (In this problem, an informal description of the sets or a picture, is ok.)oleviupo na at odiodw yee S vip to the ot to nosimob tiilqxo me ovignoitalot oonoleviupo na esaslo 0 < bas 0 <3 li vino bus lig sa
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- In Problems 17 , find a linear mapping that maps the set S onto the set S'. (Note: there may be more than one linear mapping that works.)4. Problem(4)(weight30%)TrueorFalse?(Ifthegivenstatementistrue,provideaproof,butifthestatementisfalse,giveTWO examples showingthatitisfalse.)(a) Asystemoflinearequationswithfewerequationsthanvariablescannot haveauniquesolution.(b) Forvectors ~a, ~b and ~c, if ~a ~b = ~a ~c and ~a 6= ~0 then ~b = ~c.The dependencies between the 10 activities listed in the table above are as follows:• The project starts with two activities—A, and B—which can be done concurrently.• When activity A is finished, activity C can start• When activity B is finished, activities D and E can start• When both activities C and D are finished, activity F can start• When activity E is finished, activity G can start• When activity F is finished, activity H can start• When both activities G and H are finished, activity I can start• When activity G is finished, activity J can start• The project is complete when activities I and J are finished Questions1. Organize the information above in an activity precedence table showing the activity, precedent and duration (calculated using the PERT weighted average formula and round to the nearest integer).2. Draw an AON network diagram and calculate its early start, early finish, late start and late finish times, floats (Free and total) for each activity. Make sure you…
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