You want a single fragment with both. You want a fragment with two, unlike sticky ends to favor recombination with other fragments. You want to produce fragments with two unlike sticky-ends to favor recombination. You are interested in using the plasmid p WEE as a vector for incorporating foreign DNA into E. coli where it can be cloned. The recognition sequences of the four enzymes are shown to the right.
Arrows show where the phosphodiester bonds are broken.