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Spanish: deducing a rule out of set of examples

Consider the following Spanish words, written in IPA (with their English translation):

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And the same question for middle position and final position

My answer is:

  1. Initial position: Looking at the given words, I can deduce that if an "R sound" appears in an initial position, ̃r muse be used.
  2. For same reasons, ɾ must be used at the end of a word.
  3. As for middle position, one can see that both of the consonants appear.

Is that correct?

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My answer is:

Observing that only one consonant appear at the initial/final position and that changing one with another at middle position changes word's meaning (i.e. (1) and (10)), my conclusion is that ɾ and ̃r are two different phonemes and not allophones of one phoneme. Is my analysis correct?

Thanks!