The keywords @both and @allsorted are mutually exclusive.

Left-sorted Bongard Problems have the keyword "both" on the OEBP.

The archetypal example is "rhombuses vs. rectangles".

Notice "rhombuses vs. rectangles" could alternatively be interpreted as "not rectangles vs. not rhombuses"; by this less natural interpretation, a square would fit on neither side (keyword @neither) rather than both.

In fact, for any Bongard Problem solution "A vs. B", there are three alternative solution descriptions: "A vs. not A", "not B vs. B", and "not B vs. not A". These are not necessarily just different wordings of the same answer. For example, "rhombuses vs. not rhombuses" and "not rectangles vs. rectangles" differ on where they would sort a square. (This discrepancy between "A vs. not A" and "B vs. not B" occurs whenever "A vs. B" does not sort all relevant cases. See the keyword @allsorted.)

"Is a rhombus" and "is a rectangle" are what are on the OEBP called "narrow" patterns, while "is not a rectangle" and "is not a rhombus" are not. (See keywords @left-narrow and @right-narrow for more explanation.)

Left-sorted Bongard Problems have the keyword "both" on the OEBP.

The archetypal example is "rhombuses vs. rectangles".

Notice "rhombuses vs. rectangles" could alternatively be interpreted as "not rectangles vs. not rhombuses"; by this less natural interpretation, a square would fit on neither side (keyword "neither" left-BP1189) rather than both.

In fact, for any Bongard Problem solution "A vs. B", there are three alternative solution descriptions: "A vs. not A", "not B vs. B", and "not B vs. not A". These are not necessarily just different wordings of the same answer. For example, "rhombuses vs. not rhombuses" and "not rectangles vs. rectangles" differ on where they would sort a square. (This discrepancy between "A vs. not A" and "B vs. not B" occurs whenever "A vs. B" does not sort all relevant cases. See the keyword "allsorted", left-BP509.)

"Is a rhombus" and "is a rectangle" are what are on the OEBP called "narrow" patterns, while "is not a rectangle" and "is not a rhombus" are not. (See keywords "left-narrow" left-BP513 and "right-narrow" left-BP514 for more explanation.)

Left-sorted Bongard Problems have the keyword "both" on the OEBP.

The archetypal example is "rhombuses vs. rectangles".

Notice "rhombuses vs. rectangles" could alternatively be interpreted as "not rectangles vs. not rhombuses"; by this less natural interpretation, a square would fit on neither side (keyword "neither" left-BP1189) rather than both.

In fact, for any Bongard Problem solution "A vs. B", there are three alternative solution descriptions: "A vs. not A", "not B vs. B", and "not B vs. not A". These are not necessarily just different wordings of the same answer. For example, "rhombuses vs. not rhombuses" and "not rectangles vs. rectangles" differ on where they would sort a square. (This discrepancy between "A vs. not A" and "B vs. not B" occurs whenever "A vs. B" does not sort all relevant cases. See the keyword "allsorted", left-BP509.)

"Is a rectangle vs. is a rhombus" is intuitively simplest. "Is a rectangle" and "is a rhombus" are what are on the OEBP called "narrow" patterns, while "is not a rectangle" and "is not a rhombus" are not. (See keywords "left-narrow" left-BP513 and "right-narrow" left-BP514 for further explanation.)

The keywords "both" and "allsorted" (left-BP509) are mutually exclusive.

Left-sorted Bongard Problems have the keyword "both" on the OEBP.

The archetypal example is "rhombuses vs. rectangles".

Notice "rhombuses vs. rectangles" could alternatively be interpreted as "not rectangles vs. not rhombuses"; by this less natural interpretation, a square would fit on neither side (keyword "neither" left-BP1189) rather than both.

In fact, for any Bongard Problem solution "A vs. B", there are three alternative solution descriptions: "A vs. not A", "not B vs. B", and "not B vs. not A". These are not necessarily just different wordings of the same answer. For example, "rhombuses vs. not rhombuses" and "not rectangles vs. rectangles" differ on where they would sort a square. (This discrepancy between "A vs. not A" and "B vs. not B" occurs whenever "A vs. B" does not sort all relevant cases. See the keyword "allsorted", left-BP509.)

But "is a rectangle vs. is a rhombus" seems obviously simplest. "Is a rectangle" and "is a rhombus" are what are on the OEBP called "narrow" patterns, while "is not a rectangle" and "is not a rhombus" are not. (See keywords "left-narrow" left-BP513 and "right-narrow" left-BP514 for further explanation.)

Left-sorted Bongard Problems have the keyword "both" on the OEBP.

The archetypal example is "rhombuses vs. rectangles".

Notice "rhombuses vs. rectangles" could alternatively be interpreted as "not rectangles vs. not rhombuses"; by this less natural interpretation, a square would fit on neither side (keyword "neither" left-BP1189) rather than both.

In fact, for any Bongard Problem solution "A vs. B", there are three alternative solution descriptions: "A vs. not A", "not B vs. B", and "not B vs. not A". These are not necessarily just different wordings of the same answer. For example, "rhombuses vs. not rhombuses" and "not rectangles vs. rectangles" differ on where they would sort a square. (This discrepancy between "A vs. not A" and "B vs. not B" occurs whenever "A vs. B" does not sort all relevant cases. See the keyword "allsorted", left-BP509.)

However, just one of these four alternatives seems obviously simplest. "Is a rectangle" and "is a rhombus" are what are on the OEBP called "narrow" patterns, while "is not a rectangle" and "is not a rhombus" are not. (See keywords "left-narrow" left-BP513 and "right-narrow" left-BP514 for further explanation.)

Left-sorted Bongard Problems have the keyword "both" on the OEBP.

The archetypal example is "rhombuses vs. rectangles".

Notice "rhombuses vs. rectangles" could alternatively be interpreted as "not rectangles vs. not rhombuses"; by this less natural interpretation, a square would fit on neither side (keyword "neither", left-BP1189) rather than both.

In fact, for any Bongard Problem solution "A vs. B", there are three alternative solution descriptions: "A vs. not A", "not B vs. B", and "not B vs. not A". These are not necessarily just different wordings of the same answer. For example, "rhombuses vs. not rhombuses" and "not rectangles vs. rectangles" differ on where they would sort a square. (This discrepancy between "A vs. not A" and "B vs. not B" occurs whenever "A vs. B" does not sort all relevant cases. See the keyword "allsorted", left-BP509.)

However, just one of these four alternatives seems obviously simplest. "Is a rectangle" and "is a rhombus" are what are on the OEBP called "narrow" patterns, while "is not a rectangle" and "is not a rhombus" are not. (See keywords "left-narrow" left-BP513 and "right-narrow" left-BP514 for further explanation.)

"Both" and "allsorted" (left-BP509) are mutually exclusive.

Left-sorted Bongard Problems have the keyword "both" on the OEBP.

The archetypal example is "rhombuses vs. rectangles".

Notice "rhombuses vs. rectangles" could alternatively be interpreted as "not rectangles vs. not rhombuses"; by this less natural interpretation, a square would fit on neither side rather than both.

In fact, for any Bongard Problem solution "A vs. B", there are three alternative solution descriptions: "A vs. not A", "not B vs. B", and "not B vs. not A". These are not necessarily just different wordings of the same answer. For example, "rhombuses vs. not rhombuses" and "not rectangles vs. rectangles" differ on where they would sort a square. (This discrepancy between "A vs. not A" and "B vs. not B" occurs whenever "A vs. B" does not sort all relevant cases. See the keyword "allsorted", left-BP509.)

However, just one of these four alternatives seems obviously simplest. "Is a rectangle" and "is a rhombus" are what are on the OEBP called "narrow" patterns, while "is not a rectangle" and "is not a rhombus" are not. (See keywords "left-narrow" left-BP513 and "right-narrow" left-BP514 for further explanation.)

Bongard Problems where there exists an overlap between the collections shown left and right vs. other Bongard Problems.

Left-sorted Bongard Problems have the keyword "boths" on the OEBP.

The archetypal example is "rhombuses vs. rectangles".

Notice "rhombuses vs. rectangles" could alternatively be interpreted as "not rectangles vs. not rhombuses"; by this less natural interpretation, a square would fit on neither side rather than both.

In fact, for any Bongard Problem solution "A vs. B", there are three alternative solution descriptions: "A vs. not A", "not B vs. B", and "not B vs. not A". These are not necessarily just different wordings of the same answer. For example, "rhombuses vs. not rhombuses" and "not rectangles vs. rectangles" differ on where they would sort a square. (This discrepancy between "A vs. not A" and "B vs. not B" occurs whenever "A vs. B" does not sort all relevant cases. See the keyword "allsorted", left-BP509.)

However, just one of these four alternatives seems obviously simplest. "Is a rectangle" and "is a rhombus" are what are on the OEBP called "narrow" patterns, while "is not a rectangle" and "is not a rhombus" are not. (See keywords "left-narrow" left-BP513 and "right-narrow" left-BP514 for further explanation.)

"Boths" and "allsorted" (left-BP509) are mutually exclusive.

Aaron David Fairbanks