It wouldn't be worth an answer if the bad logic wasn't foisted on us by conversational "rules" that we English speakers usually follow.
It's hard to know if the violation of conversational principles, the ill-formedness of the major premise, or the ridiculousness of the minor premise is more egregious.
1) The question sounds rhetorical. We're asked to assume that the premise is true by the way the syllogism isn't stated but implied. "Yeah, that's true--we have inflation, no minimum wage increases, so the premise must be false and minimum wage increases have nothing to do with inflation." Perhaps that's true. Something besides rhetoric would be nice. Even a bald-faced assertion would be preferable because then it would be an assertion that could be tested. Instead, it's just weaselly.
2. The underlying assumption is logic something like "If A causes C, and there's no A, there cannot be C.
"If MW wage increase causes inflation, and there's no MW wage increase, there can be no inflation."
Try this:
"If bacteria cause sickness, and there's no bacterial infection, there can be no sickness." Does the flu count as sickness? It's viral, not bacterial.
We're asked to understand the first part to be "If only minimum wage increases cause inflation . . .". The problem being that nobody makes that assertion, so it's actually underlyingly a straw man argument. The implicated assertion being argued against isn't worth arguing against.
3. Even the conclusion we're asked to reach is, on the surface, ridiculous. It's fairly obvious there are lots of reasons for "inflation"--esp. if you define it as just "price increases." Rather like my example of sickness all being bacterial in origin. Without much thought, most 9th-graders should come up with bacterial and viral infections; some will come up with other infectious agents, like parasites or fungal infections, or even protists, while others will point out that chemical toxicity can also make you sick and that sickness need not involve infection.
Let's not confuse form and substance. The real question is whether minimum wage increases actually cause inflation (with other questions like whether they reduce efficiency, growth, etc.). The answer is hard because typically we're more likely to increase the MW when the economy is growing and wages are, in general, rising anyway. Then what we do is compare growth against a model--and since there have been various models over time, with competing assumptions, it's hard to make a convincing argument.
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