It's a bit academic, but set theory doesn't really apply to such fuzzy human things as knowledge and experience. Repairing and designing are different pursuits which might have a lot of similarities, but I wouldn't presume that a design engineer could competently do the work of a technician.
Just consider that any particular field of engineering as might be described by a lay person, can be far too broad and deep for an individual to be competent in all facets of it. I'm reminded of my neighbour asking for some help configuring email for her new iPhone, because she knows I do computer work. Mainly firmware.
repair and design have in common that they require a lot of hard thought about the causal relationships involved in making the artifact work, tracing the causal chains through until they break, then patching them up. but they both also certainly involve other skills that the other does not; design also requires figuring out how to make new things happen, which involves imagining things that have never happened, while repair also requires knowing how not to bust your knuckles or spill the gasoline
(i mean, if all the parts of your engine are trashed, you are going to have to machine replacements for them, and that might actually take you longer. but it's clearly achievable given that people have built internal combustion engines without a working example to take measurements from)