(a) let x be the space obtained by forming the con- nected sum of two infinite cylinders. show that x is homotopy equivalent to a union of two circles which intersect at two points (just like, for exam- ple, two different great circles on the sphere) (b) suppose instead that x is obtained by taking the connected sum of two möbius strips (where the disks we cut out of these möbius strips do not touch the boundary). is x homotopy equivalent to some union of curves, as in the first part of this problem? if so, describe it.