Is this statement a tautology: “If there were no opportunities there would be no crimes” ?

It depends on how strictly you want to define the word “tautology”.

A) FORMAL: If you wanted to evaluate it this statement as a formal tautology you would have to rewrite it as a formal statement first. In the form

“IF NOT a THEN NOT b”
(a=opportunities, b=crimes)
it is not a tautology, but in the form

“IF NOT a THEN NOT (a AND b)”
(a=opportunities, b=actions and opportunities + actions=crimes)

it is a tautology, because no possible assignment of a and b makes the statement as a whole false.

B) RHETORICAL
Although, taken literally, it seems to verge on a tautology in a rhetorical sense, you could reasonably argue that it functions rhetorically as a stand-in for the substantive claim “preventing opportunities is the best way to prevent crimes”.

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