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I write a paper that defines a certain algorithm on geometric shapes. I have a sentence similar to the following:

If the input to the algorithm is connected, convex or rectangular, then its output will also be connected, convex or rectangular, respectively.

What I mean is that:

  • If the input is a connected shape, then the output will be a connected shape.
  • If the input is a convex shape, then the output will be a convex shape.
  • If the input is a rectangular shape, then the output will be a rectangular shape.

Note that all rectangular shapes are also convex, and all convex shapes are also connected, so the elements in the conjunction contain one another. Therefore, the word "or" seems strange in this context. Can you suggest a better way to express this meaning?

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    Perhaps something more or less like: "The output of this algorithm will have the same corresponding shape of its input, which can be one of the following shapes: connected, convex, rectangular."
    – F.E.
    Dec 11, 2013 at 19:18
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    "Connectedness, convexity, and rectangularity are preserved from input to output"
    – nohat ♦
    Dec 11, 2013 at 19:24

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There is nothing wrong with what you proposed. Without tediously writing three sentences, this is properly expressed. The use of "respectively" makes it absolutely clear what you mean.

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